Rusakov, O. V.; Yakubovich, Yu. V.; Baev, B. A. On some local asymptotic properties of sequences with a random index. (English. Russian original) Zbl 07311063 Vestn. St. Petersbg. Univ., Math. 53, No. 3, 308-319 (2020); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 7(65), No. 3, 453-468 (2020). MSC: 60 28A 28 PDF BibTeX XML Cite \textit{O. V. Rusakov} et al., Vestn. St. Petersbg. Univ., Math. 53, No. 3, 308--319 (2020; Zbl 07311063); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 7(65), No. 3, 453--468 (2020) Full Text: DOI
Michelitsch, Thomas M.; Riascos, Alejandro P. Generalized fractional Poisson process and related stochastic dynamics. (English) Zbl 07268197 Fract. Calc. Appl. Anal. 23, No. 3, 656-693 (2020). MSC: 60K05 33E12 26A33 60J60 65R10 60K40 PDF BibTeX XML Cite \textit{T. M. Michelitsch} and \textit{A. P. Riascos}, Fract. Calc. Appl. Anal. 23, No. 3, 656--693 (2020; Zbl 07268197) Full Text: DOI
Ma, Fangli; Tan, Zhongquan The point process of upcrossings formed by storage process with fractional Brownian motion as input. (English) Zbl 07266391 Adv. Math., Beijing 49, No. 2, 241-252 (2020). MSC: 60G55 60G70 60G22 PDF BibTeX XML Cite \textit{F. Ma} and \textit{Z. Tan}, Adv. Math., Beijing 49, No. 2, 241--252 (2020; Zbl 07266391) Full Text: DOI
Kumar, Arun; Leonenko, Nikolai; Pichler, Alois Fractional risk process in insurance. (English) Zbl 1435.91156 Math. Financ. Econ. 14, No. 1, 43-65 (2020). Reviewer: Jonas Šiaulys (Vilnius) MSC: 91G05 60G22 60K05 PDF BibTeX XML Cite \textit{A. Kumar} et al., Math. Financ. Econ. 14, No. 1, 43--65 (2020; Zbl 1435.91156) Full Text: DOI
Dhanalakshmi, K.; Balasubramaniam, P. Stability result of higher-order fractional neutral stochastic differential system with infinite delay driven by Poisson jumps and Rosenblatt process. (English) Zbl 1440.60049 Stochastic Anal. Appl. 38, No. 2, 352-372 (2020). MSC: 60H10 60H05 34A08 45M10 PDF BibTeX XML Cite \textit{K. Dhanalakshmi} and \textit{P. Balasubramaniam}, Stochastic Anal. Appl. 38, No. 2, 352--372 (2020; Zbl 1440.60049) Full Text: DOI
Sengar, Ayushi S.; Maheshwari, A.; Upadhye, N. S. Time-changed Poisson processes of order \(k\). (English) Zbl 1427.60091 Stochastic Anal. Appl. 38, No. 1, 124-148 (2020). MSC: 60G55 60G51 60G22 PDF BibTeX XML Cite \textit{A. S. Sengar} et al., Stochastic Anal. Appl. 38, No. 1, 124--148 (2020; Zbl 1427.60091) Full Text: DOI arXiv
Liu, Hailing; Xu, Liping; Li, Zhi Stochastic differential equations driven by multi-fractional Brownian motion and Poisson point process. (English) Zbl 1449.60107 J. Partial Differ. Equations 32, No. 4, 352-368 (2019). MSC: 60H15 60G22 60G55 PDF BibTeX XML Cite \textit{H. Liu} et al., J. Partial Differ. Equations 32, No. 4, 352--368 (2019; Zbl 1449.60107) Full Text: DOI
Shokrollahi, Foad Pricing compound and extendible options under mixed fractional Brownian motion with jumps. (English) Zbl 1432.91125 Axioms 8, No. 2, Paper No. 39, 12 p. (2019). MSC: 91G20 60G22 60H30 PDF BibTeX XML Cite \textit{F. Shokrollahi}, Axioms 8, No. 2, Paper No. 39, 12 p. (2019; Zbl 1432.91125) Full Text: DOI
Grecksch, Wilfried; Lisei, Hannelore; Lueddeckens, Jens Parameter estimations for linear parabolic fractional SPDEs with jumps. (English) Zbl 1438.60088 Stud. Univ. Babeş-Bolyai, Math. 64, No. 2, 279-289 (2019). MSC: 60H15 62F12 60G22 PDF BibTeX XML Cite \textit{W. Grecksch} et al., Stud. Univ. Babeş-Bolyai, Math. 64, No. 2, 279--289 (2019; Zbl 1438.60088) Full Text: DOI
Araya, Héctor; Bahamonde, Natalia; Torres, Soledad; Viens, Frederi Donsker type theorem for fractional Poisson process. (English) Zbl 07101597 Stat. Probab. Lett. 150, 1-8 (2019). MSC: 60F17 60G22 60G50 PDF BibTeX XML Cite \textit{H. Araya} et al., Stat. Probab. Lett. 150, 1--8 (2019; Zbl 07101597) Full Text: DOI
Kataria, K. K.; Vellaisamy, P. On distributions of certain state-dependent fractional point processes. (English) Zbl 1432.60046 J. Theor. Probab. 32, No. 3, 1554-1580 (2019). MSC: 60G22 60G55 PDF BibTeX XML Cite \textit{K. K. Kataria} and \textit{P. Vellaisamy}, J. Theor. Probab. 32, No. 3, 1554--1580 (2019; Zbl 1432.60046) Full Text: DOI
Maheshwari, A.; Vellaisamy, P. Fractional Poisson process time-changed by Lévy subordinator and its inverse. (English) Zbl 07081636 J. Theor. Probab. 32, No. 3, 1278-1305 (2019). MSC: 60G22 60G55 PDF BibTeX XML Cite \textit{A. Maheshwari} and \textit{P. Vellaisamy}, J. Theor. Probab. 32, No. 3, 1278--1305 (2019; Zbl 07081636) Full Text: DOI
Leonenko, Nikolai; Scalas, Enrico; Trinh, Mailan Limit theorems for the fractional nonhomogeneous Poisson process. (English) Zbl 1418.60025 J. Appl. Probab. 56, No. 1, 246-264 (2019). MSC: 60F17 60F05 60G55 PDF BibTeX XML Cite \textit{N. Leonenko} et al., J. Appl. Probab. 56, No. 1, 246--264 (2019; Zbl 1418.60025) Full Text: DOI arXiv
Gatheral, Jim; Keller-Ressel, Martin Affine forward variance models. (English) Zbl 1430.91110 Finance Stoch. 23, No. 3, 501-533 (2019). Reviewer: Tak Kuen Siu (Sydney) MSC: 91G20 60G22 60G55 PDF BibTeX XML Cite \textit{J. Gatheral} and \textit{M. Keller-Ressel}, Finance Stoch. 23, No. 3, 501--533 (2019; Zbl 1430.91110) Full Text: DOI arXiv
Valdivia, Arturo Closed-form formulas for the distribution of the jumps of doubly-stochastic Poisson processes. (English) Zbl 1412.60060 Electron. Commun. Probab. 24, Paper No. 13, 12 p. (2019). MSC: 60G22 60G51 60H07 91G40 PDF BibTeX XML Cite \textit{A. Valdivia}, Electron. Commun. Probab. 24, Paper No. 13, 12 p. (2019; Zbl 1412.60060) Full Text: DOI Euclid arXiv
Maheshwari, A.; Vellaisamy, P. Non-homogeneous space-time fractional Poisson processes. (English) Zbl 07054768 Stochastic Anal. Appl. 37, No. 2, 137-154 (2019). MSC: 60G22 60G55 PDF BibTeX XML Cite \textit{A. Maheshwari} and \textit{P. Vellaisamy}, Stochastic Anal. Appl. 37, No. 2, 137--154 (2019; Zbl 07054768) Full Text: DOI arXiv
Cheung, Eric C. K.; Rabehasaina, Landy; Woo, Jae-Kyung; Xu, Ran Asymptotic correlation structure of discounted incurred but not reported claims under fractional Poisson arrival process. (English) Zbl 1430.90188 Eur. J. Oper. Res. 276, No. 2, 582-601 (2019). MSC: 90B22 60K10 60G22 PDF BibTeX XML Cite \textit{E. C. K. Cheung} et al., Eur. J. Oper. Res. 276, No. 2, 582--601 (2019; Zbl 1430.90188) Full Text: DOI
Polito, Federico Studies on generalized Yule models. (English) Zbl 1426.60057 Mod. Stoch., Theory Appl. 6, No. 1, 41-55 (2019). MSC: 60G55 60J80 60G22 PDF BibTeX XML Cite \textit{F. Polito}, Mod. Stoch., Theory Appl. 6, No. 1, 41--55 (2018; Zbl 1426.60057) Full Text: DOI arXiv
Kumar, Arun; Nane, Erkan On the infinite divisibility of distributions of some inverse subordinators. (English) Zbl 1426.60018 Mod. Stoch., Theory Appl. 5, No. 4, 509-519 (2018). MSC: 60E07 PDF BibTeX XML Cite \textit{A. Kumar} and \textit{E. Nane}, Mod. Stoch., Theory Appl. 5, No. 4, 509--519 (2018; Zbl 1426.60018) Full Text: DOI arXiv
Sang, Liheng; Shen, Guangjun; Wang, Qingbo Weak convergence of the complex fractional Brownian motion. (English) Zbl 1448.60092 Adv. Difference Equ. 2018, Paper No. 444, 18 p. (2018). MSC: 60G22 60F05 60G15 26A33 60G65 PDF BibTeX XML Cite \textit{L. Sang} et al., Adv. Difference Equ. 2018, Paper No. 444, 18 p. (2018; Zbl 1448.60092) Full Text: DOI
Vellaisamy, Palaniappan; Maheshwari, Aditya Fractional negative binomial and Pólya processes. (English) Zbl 1410.60043 Probab. Math. Stat. 38, No. 1, 77-101 (2018). MSC: 60G22 60G51 PDF BibTeX XML Cite \textit{P. Vellaisamy} and \textit{A. Maheshwari}, Probab. Math. Stat. 38, No. 1, 77--101 (2018; Zbl 1410.60043) Full Text: Link
Iacus, Stefano M.; Yoshida, Nakahiro Simulation and inference for stochastic processes with YUIMA. A comprehensive R framework for SDEs and other stochastic processes. (English) Zbl 06905113 Use R!. Cham: Springer (ISBN 978-3-319-55567-6/pbk; 978-3-319-55569-0/ebook). xiii, 268 p. (2018). Reviewer: Irina Ioana Mohorianu (Oxford) MSC: 60-02 60-04 60G05 68N15 PDF BibTeX XML Cite \textit{S. M. Iacus} and \textit{N. Yoshida}, Simulation and inference for stochastic processes with YUIMA. A comprehensive R framework for SDEs and other stochastic processes. Cham: Springer (2018; Zbl 06905113) Full Text: DOI
Víquez R, Juan José Normal convergence using Malliavin calculus with applications and examples. (English) Zbl 1390.60197 Stochastic Anal. Appl. 36, No. 2, 341-372 (2018). MSC: 60H07 PDF BibTeX XML Cite \textit{J. J. Víquez R}, Stochastic Anal. Appl. 36, No. 2, 341--372 (2018; Zbl 1390.60197) Full Text: DOI
Lizama, Carlos; Rebolledo, Rolando A semigroup approach to fractional Poisson processes. (English) Zbl 1390.39028 Complex Anal. Oper. Theory 12, No. 3, 777-785 (2018). MSC: 39A13 39A14 39A06 39A60 47D06 47D99 PDF BibTeX XML Cite \textit{C. Lizama} and \textit{R. Rebolledo}, Complex Anal. Oper. Theory 12, No. 3, 777--785 (2018; Zbl 1390.39028) Full Text: DOI
Alrawashdeh, Mahmoud S.; Kelly, James F.; Meerschaert, Mark M.; Scheffler, Hans-Peter Applications of inverse tempered stable subordinators. (English) Zbl 1409.60058 Comput. Math. Appl. 73, No. 6, 892-905 (2017). MSC: 60G22 60G55 35R11 PDF BibTeX XML Cite \textit{M. S. Alrawashdeh} et al., Comput. Math. Appl. 73, No. 6, 892--905 (2017; Zbl 1409.60058) Full Text: DOI
Antunes, Nelson; Pipiras, Vladas; Abry, Patrice; Veitch, Darryl Small and large scale behavior of moments of Poisson cluster processes. (English) Zbl 1393.60051 ESAIM, Probab. Stat. 21, 369-393 (2017). MSC: 60G55 60G18 60K30 60G22 PDF BibTeX XML Cite \textit{N. Antunes} et al., ESAIM, Probab. Stat. 21, 369--393 (2017; Zbl 1393.60051) Full Text: DOI
Li, Mengyu; Shen, Guangjun; Cui, Jing Weak approximation for a class of multidimensional parameter Gaussian process. (Chinese. English summary) Zbl 1399.60028 J. Math., Wuhan Univ. 37, No. 6, 1287-1302 (2017). MSC: 60F05 60G15 PDF BibTeX XML Cite \textit{M. Li} et al., J. Math., Wuhan Univ. 37, No. 6, 1287--1302 (2017; Zbl 1399.60028) Full Text: DOI
Liu, Junfeng; Sun, Xichao Weak convergence to the two-parameter Volterra multifractional process in Besov spaces. (English) Zbl 1399.60030 J. Math. Res. Appl. 37, No. 5, 619-630 (2017). MSC: 60F05 60G22 60G51 PDF BibTeX XML Cite \textit{J. Liu} and \textit{X. Sun}, J. Math. Res. Appl. 37, No. 5, 619--630 (2017; Zbl 1399.60030) Full Text: DOI
Di Crescenzo, Antonio; Meoli, Alessandra On a fractional alternating Poisson process. (English) Zbl 1426.60101 AIMS Math. 1, No. 3, 212-224 (2016). MSC: 60J25 60G55 60G22 34A08 PDF BibTeX XML Cite \textit{A. Di Crescenzo} and \textit{A. Meoli}, AIMS Math. 1, No. 3, 212--224 (2016; Zbl 1426.60101) Full Text: DOI
Shen, Guangjun; Sang, Liheng; Dai, Hongshuai Weak convergence to multifractional Brownian sheet of Riemann-Liouville type in Besov spaces. (English) Zbl 1374.60026 Math. Appl. 29, No. 4, 749-760 (2016). MSC: 60F05 60G22 PDF BibTeX XML Cite \textit{G. Shen} et al., Math. Appl. 29, No. 4, 749--760 (2016; Zbl 1374.60026)
Maheshwari, A.; Vellaisamy, P. On the long-range dependence of fractional Poisson and negative binomial processes. (English) Zbl 1355.60052 J. Appl. Probab. 53, No. 4, 989-1000 (2016). MSC: 60G22 60G55 PDF BibTeX XML Cite \textit{A. Maheshwari} and \textit{P. Vellaisamy}, J. Appl. Probab. 53, No. 4, 989--1000 (2016; Zbl 1355.60052) Full Text: DOI Euclid arXiv
Sebastian, Nicy; Gorenflo, Rudolf Time series models associated with Mittag-Leffler type distributions and its properties. (English) Zbl 1357.60042 Commun. Stat., Theory Methods 45, No. 24, 7210-7225 (2016). MSC: 60G22 60K05 26A33 62M10 62E15 33E12 PDF BibTeX XML Cite \textit{N. Sebastian} and \textit{R. Gorenflo}, Commun. Stat., Theory Methods 45, No. 24, 7210--7225 (2016; Zbl 1357.60042) Full Text: DOI
Chen, Zhen-Qing; Ren, Yan-Xia; Yang, Ting Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators. (English) Zbl 1351.60105 Potential Anal. 45, No. 3, 509-537 (2016). MSC: 60J45 31B05 31B25 PDF BibTeX XML Cite \textit{Z.-Q. Chen} et al., Potential Anal. 45, No. 3, 509--537 (2016; Zbl 1351.60105) Full Text: DOI arXiv
Orsingher, Enzo; Ricciuti, Costantino; Toaldo, Bruno Time-inhomogeneous jump processes and variable order operators. (English) Zbl 1361.60075 Potential Anal. 45, No. 3, 435-461 (2016). Reviewer: Nicolas Privault (Singapore) MSC: 60J75 60G51 60G55 60J65 PDF BibTeX XML Cite \textit{E. Orsingher} et al., Potential Anal. 45, No. 3, 435--461 (2016; Zbl 1361.60075) Full Text: DOI arXiv
Orsingher, Enzo; Ricciuti, Costantino; Toaldo, Bruno Population models at stochastic times. (English) Zbl 1344.60083 Adv. Appl. Probab. 48, No. 2, 481-498 (2016). MSC: 60J80 60G22 60G55 92D25 PDF BibTeX XML Cite \textit{E. Orsingher} et al., Adv. Appl. Probab. 48, No. 2, 481--498 (2016; Zbl 1344.60083) Full Text: DOI Link arXiv
Lakhel, El Hassan Exponential stability for stochastic neutral functional differential equations driven by Rosenblatt process with delay and Poisson jumps. (English) Zbl 1338.60159 Random Oper. Stoch. Equ. 24, No. 2, 113-127 (2016). MSC: 60H15 60H10 60H20 34K50 60G55 60G18 60G22 PDF BibTeX XML Cite \textit{E. H. Lakhel}, Random Oper. Stoch. Equ. 24, No. 2, 113--127 (2016; Zbl 1338.60159) Full Text: DOI
Di Crescenzo, Antonio; Martinucci, Barbara; Meoli, Alessandra A fractional counting process and its connection with the Poisson process. (English) Zbl 1337.60063 ALEA, Lat. Am. J. Probab. Math. Stat. 13, No. 1, 291-307 (2016). MSC: 60G22 60G55 60G40 60J80 34A08 PDF BibTeX XML Cite \textit{A. Di Crescenzo} et al., ALEA, Lat. Am. J. Probab. Math. Stat. 13, No. 1, 291--307 (2016; Zbl 1337.60063) Full Text: Link arXiv
Gorenflo, Rudolf; Mainardi, Francesco On the fractional Poisson process and the discretized stable subordinator. (English) Zbl 1415.60051 Axioms 4, No. 3, 321-344 (2015). MSC: 60G55 60G22 60K05 PDF BibTeX XML Cite \textit{R. Gorenflo} and \textit{F. Mainardi}, Axioms 4, No. 3, 321--344 (2015; Zbl 1415.60051) Full Text: DOI
Prakasa Rao, B. L. S. Filtered fractional Poisson processes. (English) Zbl 07035740 Stat. Methodol. 26, 124-134 (2015). MSC: 60G22 33E12 PDF BibTeX XML Cite \textit{B. L. S. Prakasa Rao}, Stat. Methodol. 26, 124--134 (2015; Zbl 07035740) Full Text: DOI
Quéau, Pierre-Yves; Woyczyński, Wojbor A.; Lerner, Alan J. Coalescing stochastic processes in retrival from semantic memory. (English) Zbl 1371.91146 Math. Appl. (Warsaw) 43, No. 1-2, 187-224 (2015). MSC: 91E40 60G51 60G22 60J20 60J28 62F10 62P15 62G07 PDF BibTeX XML Cite \textit{P.-Y. Quéau} et al., Math. Appl. (Warsaw) 43, No. 1--2, 187--224 (2015; Zbl 1371.91146) Full Text: DOI
Cahoy, Dexter O.; Polito, Federico; Phoha, Vir Transient behavior of fractional queues and related processes. (English) Zbl 1322.60189 Methodol. Comput. Appl. Probab. 17, No. 3, 739-759 (2015). MSC: 60K25 60G22 60J80 60G55 62M05 62M09 90B22 68M20 26A33 91G80 PDF BibTeX XML Cite \textit{D. O. Cahoy} et al., Methodol. Comput. Appl. Probab. 17, No. 3, 739--759 (2015; Zbl 1322.60189) Full Text: DOI arXiv
Budhiraja, Amarjit; Pipiras, Vladas; Song, Xiaoming Admission control for multidimensional workload input with heavy tails and fractional Ornstein-Uhlenbeck process. (English) Zbl 1321.60196 Adv. Appl. Probab. 47, No. 2, 476-505 (2015). MSC: 60K30 60G57 60G55 60G15 60H10 60G22 60G18 90B15 PDF BibTeX XML Cite \textit{A. Budhiraja} et al., Adv. Appl. Probab. 47, No. 2, 476--505 (2015; Zbl 1321.60196) Full Text: DOI Euclid arXiv
Garra, R.; Orsingher, E.; Polito, F. State-dependent fractional point processes. (English) Zbl 1315.60056 J. Appl. Probab. 52, No. 1, 18-36 (2015). MSC: 60G55 60G22 60G52 34A08 26A33 PDF BibTeX XML Cite \textit{R. Garra} et al., J. Appl. Probab. 52, No. 1, 18--36 (2015; Zbl 1315.60056) Full Text: DOI Euclid arXiv
Bai, Lihua; Ma, Jin Stochastic differential equations driven by fractional Brownian motion and Poisson point process. (English) Zbl 1319.60123 Bernoulli 21, No. 1, 303-334 (2015). Reviewer: Hans Crauel (Frankfurt am Main) MSC: 60H10 60G22 60G55 60J65 PDF BibTeX XML Cite \textit{L. Bai} and \textit{J. Ma}, Bernoulli 21, No. 1, 303--334 (2015; Zbl 1319.60123) Full Text: DOI Euclid arXiv
Molchanov, Ilya; Ralchenko, Kostiantyn Multifractional Poisson process, multistable subordinator and related limit theorems. (English) Zbl 1326.60049 Stat. Probab. Lett. 96, 95-101 (2015). MSC: 60G22 60G55 60G52 60G50 60F05 PDF BibTeX XML Cite \textit{I. Molchanov} and \textit{K. Ralchenko}, Stat. Probab. Lett. 96, 95--101 (2015; Zbl 1326.60049) Full Text: DOI arXiv
Wang, Ying; Wang, Dehui; Zhu, Fukang Estimation of parameters in the fractional compound Poisson process. (English) Zbl 07175143 Commun. Nonlinear Sci. Numer. Simul. 19, No. 10, 3425-3430 (2014). MSC: 62 60 PDF BibTeX XML Cite \textit{Y. Wang} et al., Commun. Nonlinear Sci. Numer. Simul. 19, No. 10, 3425--3430 (2014; Zbl 07175143) Full Text: DOI
Mishura, Yu.; Zubchenko, V. Properties of integrals with respect to fractional Poisson processes with compact kernels. (English) Zbl 1326.60080 Theory Probab. Math. Stat. 89, 143-152 (2014); translation from Teor. Jmovirn. Mat. Stat. 89, 130–139 (2013). MSC: 60H05 60G22 60G55 60G51 PDF BibTeX XML Full Text: DOI
D’Ovidio, Mirko Continuous random walks and fractional powers of operators. (English) Zbl 1308.60053 J. Math. Anal. Appl. 411, No. 1, 362-371 (2014). MSC: 60G50 60G52 35R60 PDF BibTeX XML Cite \textit{M. D'Ovidio}, J. Math. Anal. Appl. 411, No. 1, 362--371 (2014; Zbl 1308.60053) Full Text: DOI arXiv
Beghin, Luisa; D’Ovidio, Mirko Fractional Poisson process with random drift. (English) Zbl 1334.60053 Electron. J. Probab. 19, Paper No. 122, 26 p. (2014). MSC: 60G22 60G55 60G51 35R11 60G50 60G35 PDF BibTeX XML Cite \textit{L. Beghin} and \textit{M. D'Ovidio}, Electron. J. Probab. 19, Paper No. 122, 26 p. (2014; Zbl 1334.60053) Full Text: DOI arXiv
Kerss, Alexander; Leonenko, Nikolai N.; Sikorskii, Alla Fractional Skellam processes with applications to finance. (English) Zbl 1310.60034 Fract. Calc. Appl. Anal. 17, No. 2, 532-551 (2014). MSC: 60G22 60E05 60G51 26A33 PDF BibTeX XML Cite \textit{A. Kerss} et al., Fract. Calc. Appl. Anal. 17, No. 2, 532--551 (2014; Zbl 1310.60034) Full Text: DOI
Biard, Romain; Saussereau, Bruno Fractional Poisson process: long-range dependence and applications in ruin theory. (English) Zbl 1312.60042 J. Appl. Probab. 51, No. 3, 727-740 (2014); correction 53, No. 4, 1271-1272 (2016). MSC: 60G22 60G55 60K05 91B30 33E12 PDF BibTeX XML Cite \textit{R. Biard} and \textit{B. Saussereau}, J. Appl. Probab. 51, No. 3, 727--740 (2014; Zbl 1312.60042) Full Text: DOI Euclid
Popovic, Lea; Rivas, Mariolys The coalescent point process of multi-type branching trees. (English) Zbl 1311.60097 Stochastic Processes Appl. 124, No. 12, 4120-4148 (2014). Reviewer: P. R. Parthasarathy (Chennai) MSC: 60J80 60G55 60J85 PDF BibTeX XML Cite \textit{L. Popovic} and \textit{M. Rivas}, Stochastic Processes Appl. 124, No. 12, 4120--4148 (2014; Zbl 1311.60097) Full Text: DOI arXiv
Shevchenko, Georgiy Mixed fractional stochastic differential equations with jumps. (English) Zbl 1307.60087 Stochastics 86, No. 2, 203-217 (2014). MSC: 60H10 60G22 60G15 60J65 PDF BibTeX XML Cite \textit{G. Shevchenko}, Stochastics 86, No. 2, 203--217 (2014; Zbl 1307.60087) Full Text: DOI arXiv
Garra, Roberto; Orsingher, Enzo; Polito, Federico Fractional Klein-Gordon equations and related stochastic processes. (English) Zbl 1301.35131 J. Stat. Phys. 155, No. 4, 777-809 (2014). Reviewer: Thomas Ernst (Uppsala) MSC: 35Q53 35R11 82B41 35Q05 33E12 26A33 PDF BibTeX XML Cite \textit{R. Garra} et al., J. Stat. Phys. 155, No. 4, 777--809 (2014; Zbl 1301.35131) Full Text: DOI arXiv
Lifshits, Mikhail Random processes by example. (English) Zbl 1305.60002 Hackensack, NJ: World Scientific (ISBN 978-981-4522-28-1/hbk; 978-981-4522-30-4/ebook). xi, 219 p. (2014). Reviewer: Jordan M. Stoyanov (Newcastle upon Tyne) MSC: 60-01 60G05 60G15 60G22 60G51 60G57 60H05 PDF BibTeX XML Cite \textit{M. Lifshits}, Random processes by example. Hackensack, NJ: World Scientific (2014; Zbl 1305.60002) Full Text: DOI
Wang, Yizao Convergence to the maximum process of a fractional Brownian motion with shot noise. (English) Zbl 1292.60042 Stat. Probab. Lett. 90, 33-41 (2014). MSC: 60F17 60G70 60G22 60G55 PDF BibTeX XML Cite \textit{Y. Wang}, Stat. Probab. Lett. 90, 33--41 (2014; Zbl 1292.60042) Full Text: DOI arXiv
Beghin, Luisa; Macci, Claudio Fractional discrete processes: compound and mixed Poisson representations. (English) Zbl 1294.26004 J. Appl. Probab. 51, No. 1, 19-36 (2014). MSC: 26A33 33E12 60G22 PDF BibTeX XML Cite \textit{L. Beghin} and \textit{C. Macci}, J. Appl. Probab. 51, No. 1, 19--36 (2014; Zbl 1294.26004) Full Text: DOI Euclid arXiv
Kreer, Markus; Kızılersü, Ayşe; Thomas, Anthony W. Fractional Poisson processes and their representation by infinite systems of ordinary differential equations. (English) Zbl 1302.60068 Stat. Probab. Lett. 84, 27-32 (2014). MSC: 60G22 PDF BibTeX XML Cite \textit{M. Kreer} et al., Stat. Probab. Lett. 84, 27--32 (2014; Zbl 1302.60068) Full Text: DOI arXiv
Scalas, Enrico; Viles, Noèlia A functional limit theorem for stochastic integrals driven by a time-changed symmetric \(\alpha\)-stable Lévy process. (English) Zbl 1301.60034 Stochastic Processes Appl. 124, No. 1, 385-410 (2014). MSC: 60F17 60H05 60G51 PDF BibTeX XML Cite \textit{E. Scalas} and \textit{N. Viles}, Stochastic Processes Appl. 124, No. 1, 385--410 (2014; Zbl 1301.60034) Full Text: DOI arXiv
Dombry, Clément; Kaj, Ingemar Moment measures of heavy-tailed renewal point processes: asymptotics and applications. (English) Zbl 1291.60178 ESAIM, Probab. Stat. 17, 567-591 (2013). Reviewer: Edward Omey (Brussel) MSC: 60K05 60G22 60F05 26A12 PDF BibTeX XML Cite \textit{C. Dombry} and \textit{I. Kaj}, ESAIM, Probab. Stat. 17, 567--591 (2013; Zbl 1291.60178) Full Text: DOI
Orsingher, Enzo Fractional Poisson processes. (English) Zbl 1272.60019 Sci. Math. Jpn. 76, No. 1, 139-145 (2013). MSC: 60G22 60K05 PDF BibTeX XML Cite \textit{E. Orsingher}, Sci. Math. Jpn. 76, No. 1, 139--145 (2013; Zbl 1272.60019) Full Text: Link
Beghin, Luisa; Macci, Claudio Large deviations for fractional Poisson processes. (English) Zbl 1266.60046 Stat. Probab. Lett. 83, No. 4, 1193-1202 (2013). MSC: 60F10 60G22 91B30 PDF BibTeX XML Cite \textit{L. Beghin} and \textit{C. Macci}, Stat. Probab. Lett. 83, No. 4, 1193--1202 (2013; Zbl 1266.60046) Full Text: DOI arXiv
Lambert, Amaury; Popovic, Lea The coalescent point process of branching trees. (English) Zbl 1268.60107 Ann. Appl. Probab. 23, No. 1, 99-144 (2013). Reviewer: Valentin Topchii (Omsk) MSC: 60J80 60G55 60G57 60J10 60J85 60J27 92D10 92D25 PDF BibTeX XML Cite \textit{A. Lambert} and \textit{L. Popovic}, Ann. Appl. Probab. 23, No. 1, 99--144 (2013; Zbl 1268.60107) Full Text: DOI Euclid arXiv
Dai, Hongshuai Convergence in law to operator fractional Brownian motion of Riemann-Liouville type. (English) Zbl 1263.60034 Acta Math. Sin., Engl. Ser. 29, No. 4, 777-788 (2013). MSC: 60G22 60F17 60G15 PDF BibTeX XML Cite \textit{H. Dai}, Acta Math. Sin., Engl. Ser. 29, No. 4, 777--788 (2013; Zbl 1263.60034) Full Text: DOI
Konno, Hidetoshi On the nature of fluctuations associated with fractional Poisson process. (English) Zbl 1348.60060 Adv. Stud. Theor. Phys. 6, No. 21-24, 1039-1058 (2012). MSC: 60G22 92B25 PDF BibTeX XML Cite \textit{H. Konno}, Adv. Stud. Theor. Phys. 6, No. 21--24, 1039--1058 (2012; Zbl 1348.60060) Full Text: Link
Scalas, Enrico; Viles, Noèlia On the convergence of quadratic variation for compound fractional Poisson processes. (English) Zbl 1278.60067 Fract. Calc. Appl. Anal. 15, No. 2, 314-331 (2012). Reviewer: Enzo Orsingher (Roma) MSC: 60F17 60G20 60G22 60G51 26A33 33E12 PDF BibTeX XML Cite \textit{E. Scalas} and \textit{N. Viles}, Fract. Calc. Appl. Anal. 15, No. 2, 314--331 (2012; Zbl 1278.60067) Full Text: DOI
Cahoy, Dexter O.; Polito, Federico Simulation and estimation for the fractional Yule process. (English) Zbl 1253.60090 Methodol. Comput. Appl. Probab. 14, No. 2, 383-403 (2012). MSC: 60J80 60G22 60G55 62M05 PDF BibTeX XML Cite \textit{D. O. Cahoy} and \textit{F. Polito}, Methodol. Comput. Appl. Probab. 14, No. 2, 383--403 (2012; Zbl 1253.60090) Full Text: DOI arXiv
Barbe, Ph.; McCormick, W. P. The point process approach for fractionally differentiated random walks under heavy traffic. (English) Zbl 1264.60026 Stochastic Processes Appl. 122, No. 12, 4028-4053 (2012). Reviewer: Ravi Sreenivasan (Mysore) MSC: 60F99 60G50 60G52 60G22 60K25 62M10 60G70 62P20 PDF BibTeX XML Cite \textit{Ph. Barbe} and \textit{W. P. McCormick}, Stochastic Processes Appl. 122, No. 12, 4028--4053 (2012; Zbl 1264.60026) Full Text: DOI
Sun, Qiyu; Unser, Michael Left-inverses of fractional Laplacian and sparse stochastic processes. (English) Zbl 1251.26006 Adv. Comput. Math. 36, No. 3, 399-441 (2012). MSC: 26A33 60G22 35R60 34K37 PDF BibTeX XML Cite \textit{Q. Sun} and \textit{M. Unser}, Adv. Comput. Math. 36, No. 3, 399--441 (2012; Zbl 1251.26006) Full Text: DOI arXiv
Orsingher, Enzo; Polito, Federico Compositions, random sums and continued random fractions of Poisson and fractional Poisson processes. (English) Zbl 1251.60041 J. Stat. Phys. 148, No. 2, 233-249 (2012). MSC: 60G55 60G22 PDF BibTeX XML Cite \textit{E. Orsingher} and \textit{F. Polito}, J. Stat. Phys. 148, No. 2, 233--249 (2012; Zbl 1251.60041) Full Text: DOI arXiv
Garra, Roberto; Polito, Federico Analytic solutions of fractional differential equations by operational methods. (English) Zbl 1248.35222 Appl. Math. Comput. 218, No. 21, 10642-10646 (2012). MSC: 35R11 33E12 PDF BibTeX XML Cite \textit{R. Garra} and \textit{F. Polito}, Appl. Math. Comput. 218, No. 21, 10642--10646 (2012; Zbl 1248.35222) Full Text: DOI arXiv
Hiroshima, Fumio; Lőrinczi, József; Takaesu, Toshimitsu A probabilistic representation of the ground state expectation of fractional powers of the boson number operator. (English) Zbl 1252.81091 J. Math. Anal. Appl. 395, No. 2, 437-447 (2012). MSC: 81S40 81Q05 81V70 82B31 60G22 PDF BibTeX XML Cite \textit{F. Hiroshima} et al., J. Math. Anal. Appl. 395, No. 2, 437--447 (2012; Zbl 1252.81091) Full Text: DOI
Orsingher, Enzo; Polito, Federico The space-fractional Poisson process. (English) Zbl 1270.60048 Stat. Probab. Lett. 82, No. 4, 852-858 (2012). Reviewer: Rudolf Gorenflo (Berlin) MSC: 60G22 60G55 PDF BibTeX XML Cite \textit{E. Orsingher} and \textit{F. Polito}, Stat. Probab. Lett. 82, No. 4, 852--858 (2012; Zbl 1270.60048) Full Text: DOI arXiv
Kwaśnicki, Mateusz Eigenvalues of the fractional Laplace operator in the interval. (English) Zbl 1234.35164 J. Funct. Anal. 262, No. 5, 2379-2402 (2012). MSC: 35P20 35P15 47F05 47A75 35R11 35J05 PDF BibTeX XML Cite \textit{M. Kwaśnicki}, J. Funct. Anal. 262, No. 5, 2379--2402 (2012; Zbl 1234.35164) Full Text: DOI arXiv
De Gregorio, Alessandro; Orsingher, Enzo Flying randomly in \(\mathbb R^d\) with Dirichlet displacements. (English) Zbl 1244.60090 Stochastic Processes Appl. 122, No. 2, 676-713 (2012). Reviewer: Anatoliy Pogorui (Zhytomyr) MSC: 60K15 60K99 PDF BibTeX XML Cite \textit{A. De Gregorio} and \textit{E. Orsingher}, Stochastic Processes Appl. 122, No. 2, 676--713 (2012; Zbl 1244.60090) Full Text: DOI arXiv
Meerschaert, Mark M.; Nane, Erkan; Vellaisamy, P. The fractional Poisson process and the inverse stable subordinator. (English) Zbl 1245.60084 Electron. J. Probab. 16, Paper No. 59, 1600-1620 (2011). MSC: 60K05 33E12 26A33 PDF BibTeX XML Cite \textit{M. M. Meerschaert} et al., Electron. J. Probab. 16, Paper No. 59, 1600--1620 (2011; Zbl 1245.60084) Full Text: DOI arXiv
Dombry, Clément; Kaj, Ingemar The on-off network traffic model under intermediate scaling. (English) Zbl 1235.60121 Queueing Syst. 69, No. 1, 29-44 (2011). Reviewer: Oleg K. Zakusilo (Kyïv) MSC: 60K10 60G22 60F05 60K05 90B15 90B20 PDF BibTeX XML Cite \textit{C. Dombry} and \textit{I. Kaj}, Queueing Syst. 69, No. 1, 29--44 (2011; Zbl 1235.60121) Full Text: DOI
Dai, HongShuai; Li, YuQiang A note on approximation to multifractional Brownian motion. (English) Zbl 1232.60032 Sci. China, Math. 54, No. 10, 2145-2154 (2011). MSC: 60G22 60F05 60G15 PDF BibTeX XML Cite \textit{H. Dai} and \textit{Y. Li}, Sci. China, Math. 54, No. 10, 2145--2154 (2011; Zbl 1232.60032) Full Text: DOI
Li, Yuqiang; Dai, Hongshuai Approximations of fractional Brownian motion. (English) Zbl 1230.60041 Bernoulli 17, No. 4, 1195-1216 (2011). MSC: 60G22 PDF BibTeX XML Cite \textit{Y. Li} and \textit{H. Dai}, Bernoulli 17, No. 4, 1195--1216 (2011; Zbl 1230.60041) Full Text: DOI arXiv
Cahoy, Dexter O. On the parametrization of the \(M\)-Wright function. (English) Zbl 1226.60054 Far East J. Theor. Stat. 34, No. 2, 155-164 (2011). MSC: 60G22 60E05 60F17 PDF BibTeX XML Cite \textit{D. O. Cahoy}, Far East J. Theor. Stat. 34, No. 2, 155--164 (2011; Zbl 1226.60054) Full Text: Link
Uchaikin, Vladimir V. Self-similarity, stochasticity and fractionality. (English) Zbl 1263.60033 Luo, Albert C. J. (ed.) et al., Long-range interactions, stochasticity and fractional dynamics. Dedicated to George M. Zaslavsky (1935-2008). Berlin: Springer; Beijing: Higher Education Press (ISBN 978-3-642-12342-9/hbk). Nonlinear Physical Science, 27-81 (2010). Reviewer: Peter Kern (Düsseldorf) MSC: 60G18 26A33 34A08 60G22 PDF BibTeX XML Cite \textit{V. V. Uchaikin}, in: Long-range interactions, stochasticity and fractional dynamics. Dedicated to George M. Zaslavsky (1935-2008). Berlin: Springer; Beijing: Higher Education Press. 27--81 (2010; Zbl 1263.60033) Full Text: DOI
Beghin, Luisa; Orsingher, Enzo Poisson-type processes governed by fractional and higher-order recursive differential equations. (English) Zbl 1228.60093 Electron. J. Probab. 15, Paper No. 22, 684-709 (2010). MSC: 60K05 33E12 26A33 PDF BibTeX XML Cite \textit{L. Beghin} and \textit{E. Orsingher}, Electron. J. Probab. 15, Paper No. 22, 684--709 (2010; Zbl 1228.60093) Full Text: DOI EMIS arXiv
Biermé, Hermine; Estrade, Anne; Kaj, Ingemar Self-similar random fields and rescaled random balls models. (English) Zbl 1213.60096 J. Theor. Probab. 23, No. 4, 1110-1141 (2010). Reviewer: Wolfgang Freudenberg (Cottbus) MSC: 60G60 60G55 60G18 60D05 60G20 60F05 PDF BibTeX XML Cite \textit{H. Biermé} et al., J. Theor. Probab. 23, No. 4, 1110--1141 (2010; Zbl 1213.60096) Full Text: DOI
Kabluchko, Zakhar Stationary systems of Gaussian processes. (English) Zbl 1230.60054 Ann. Appl. Probab. 20, No. 6, 2295-2317 (2010). Reviewer: B. P. Harlamov (St. Peterburg) MSC: 60G55 60G15 60G60 60G22 60G10 PDF BibTeX XML Cite \textit{Z. Kabluchko}, Ann. Appl. Probab. 20, No. 6, 2295--2317 (2010; Zbl 1230.60054) Full Text: DOI arXiv
Fasen, Vicky Modeling network traffic by a cluster Poisson input process with heavy and light-tailed file sizes. (English) Zbl 1255.90041 Queueing Syst. 66, No. 4, 313-350 (2010). MSC: 90B22 60F05 60F10 60F17 60G52 PDF BibTeX XML Cite \textit{V. Fasen}, Queueing Syst. 66, No. 4, 313--350 (2010; Zbl 1255.90041) Full Text: DOI
Intarasit, A.; Sattayatham, P. A geometric Brownian motion model with compound Poisson process and fractional stochastic volatility. (English) Zbl 1205.60083 Adv. Appl. Stat. 16, No. 1, 25-47 (2010). Reviewer: Yuliya S. Mishura (Kyïv) MSC: 60G22 60G55 PDF BibTeX XML Cite \textit{A. Intarasit} and \textit{P. Sattayatham}, Adv. Appl. Stat. 16, No. 1, 25--47 (2010; Zbl 1205.60083) Full Text: Link
Cahoy, Dexter O.; Uchaikin, Vladimir V.; Woyczynski, Wojbor A. Parameter estimation for fractional Poisson processes. (English) Zbl 1205.62118 J. Stat. Plann. Inference 140, No. 11, 3106-3120 (2010). MSC: 62M05 62F10 62F25 62M09 65C60 PDF BibTeX XML Cite \textit{D. O. Cahoy} et al., J. Stat. Plann. Inference 140, No. 11, 3106--3120 (2010; Zbl 1205.62118) Full Text: DOI
Bardina, Xavier; Bascompte, David Weak convergence towards two independent Gaussian processes from a unique Poisson process. (English) Zbl 1206.60036 Collect. Math. 61, No. 2, 191-204 (2010). Reviewer: Pavel Froněk (Praha) MSC: 60F17 60G15 60H05 PDF BibTeX XML Cite \textit{X. Bardina} and \textit{D. Bascompte}, Collect. Math. 61, No. 2, 191--204 (2010; Zbl 1206.60036) Full Text: DOI Link arXiv
Beghin, Luisa; Orsingher, Enzo Fractional Poisson processes and related planar random motions. (English) Zbl 1190.60028 Electron. J. Probab. 14, 1790-1826 (2009). MSC: 60G22 60G55 26A33 PDF BibTeX XML Cite \textit{L. Beghin} and \textit{E. Orsingher}, Electron. J. Probab. 14, 1790--1826 (2009; Zbl 1190.60028) Full Text: DOI EMIS EuDML
Balan, Raluca M. A note on a Feynman-Kac-type formula. (English) Zbl 1190.60049 Electron. Commun. Probab. 14, 252-260 (2009). MSC: 60H15 PDF BibTeX XML Cite \textit{R. M. Balan}, Electron. Commun. Probab. 14, 252--260 (2009; Zbl 1190.60049) Full Text: DOI EMIS EuDML
Fasen, Vicky; Samorodnitsky, Gennady A fluid cluster Poisson input process can look like a fractional Brownian motion even in the slow growth aggregation regime. (English) Zbl 1169.90008 Adv. Appl. Probab. 41, No. 2, 393-427 (2009). Reviewer: Evsei Morozov (Petrozavodsk) MSC: 90B22 60K25 60F17 PDF BibTeX XML Cite \textit{V. Fasen} and \textit{G. Samorodnitsky}, Adv. Appl. Probab. 41, No. 2, 393--427 (2009; Zbl 1169.90008) Full Text: DOI
Forster, Brigitte; Massopust, Peter Statistical encounters with complex B-splines. (English) Zbl 1171.41305 Constr. Approx. 29, No. 3, 325-344 (2009). Reviewer: Ljubiša Kocić (Niš) MSC: 41A15 60E05 PDF BibTeX XML Cite \textit{B. Forster} and \textit{P. Massopust}, Constr. Approx. 29, No. 3, 325--344 (2009; Zbl 1171.41305) Full Text: DOI
Uchaikin, V. V.; Cahoy, D. O.; Sibatov, R. T. Fractional processes: from Poisson to branching one. (English) Zbl 1157.60324 Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, No. 9, 2717-2725 (2008). MSC: 60G99 PDF BibTeX XML Cite \textit{V. V. Uchaikin} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, No. 9, 2717--2725 (2008; Zbl 1157.60324) Full Text: DOI
Zhang, Huayue; Bai, Lihua Dynamic mean-variance optimization under classical risk model with fractional Brownian motion perturbation. (English) Zbl 1165.60321 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11, No. 4, 589-602 (2008). MSC: 60G15 93E20 91B30 PDF BibTeX XML Cite \textit{H. Zhang} and \textit{L. Bai}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11, No. 4, 589--602 (2008; Zbl 1165.60321) Full Text: DOI
Zhao, Ou; Woodroofe, Michael On martingale approximations. (English) Zbl 1161.60010 Ann. Appl. Probab. 18, No. 5, 1831-1847 (2008). Reviewer: Klaus Schürger (Bonn) MSC: 60F05 60J10 PDF BibTeX XML Cite \textit{O. Zhao} and \textit{M. Woodroofe}, Ann. Appl. Probab. 18, No. 5, 1831--1847 (2008; Zbl 1161.60010) Full Text: DOI arXiv
Zhao, Dianli Pricing of European contingent claims on stock driven by multidimensional fractional Brown motions and Poisson processes. (Chinese. English summary) Zbl 1125.91059 Math. Appl. 20, No. 2, 386-391 (2007). MSC: 91B28 60G20 PDF BibTeX XML Cite \textit{D. Zhao}, Math. Appl. 20, No. 2, 386--391 (2007; Zbl 1125.91059)
Mallor, F.; Mateo, P.; Moler, J. A. A comparison between several adjustment models to simulated teletraffic data. (English) Zbl 1141.90012 J. Stat. Plann. Inference 137, No. 12, 3939-3953 (2007). MSC: 90B18 90C40 60K30 65C99 60K25 PDF BibTeX XML Cite \textit{F. Mallor} et al., J. Stat. Plann. Inference 137, No. 12, 3939--3953 (2007; Zbl 1141.90012) Full Text: DOI
Mainardi, Francesco; Gorenflo, Rudolf; Vivoli, Alessandro Beyond the Poisson renewal process: a tutorial survey. (English) Zbl 1115.60082 J. Comput. Appl. Math. 205, No. 2, 725-735 (2007). MSC: 60K05 60K25 26A33 33E12 45K05 47G30 60G50 60G51 60G55 PDF BibTeX XML Cite \textit{F. Mainardi} et al., J. Comput. Appl. Math. 205, No. 2, 725--735 (2007; Zbl 1115.60082) Full Text: DOI
Resnick, Sidney I. Heavy-tail phenomena. Probabilistic and statistical modeling. (English) Zbl 1152.62029 Springer Series in Operations Research and Financial Engineering. New York, NY: Springer (ISBN 0-387-24272-4/hbk). xix, 404 p. (2007). Reviewer: Yuehua Wu (Toronto) MSC: 62G32 62-02 62Pxx 62-01 PDF BibTeX XML Cite \textit{S. I. Resnick}, Heavy-tail phenomena. Probabilistic and statistical modeling. New York, NY: Springer (2007; Zbl 1152.62029) Full Text: DOI
Jumarie, Guy New stochastic fractional models for Malthusian growth, the Poissonian birth process and optimal management of populations. (English) Zbl 1130.92043 Math. Comput. Modelling 44, No. 3-4, 231-254 (2006). MSC: 92D25 60J85 93E20 60J65 92B05 PDF BibTeX XML Cite \textit{G. Jumarie}, Math. Comput. Modelling 44, No. 3--4, 231--254 (2006; Zbl 1130.92043) Full Text: DOI