Ascione, Giacomo; Mishura, Yuliya; Pirozzi, Enrica The Fokker-Planck equation for the time-changed fractional Ornstein-Uhlenbeck stochastic process. (English) Zbl 1500.60020 Proc. R. Soc. Edinb., Sect. A, Math. 152, No. 4, 1032-1057 (2022). Reviewer: B. L. S. Prakasa Rao (Hyderabad) MSC: 60G22 PDFBibTeX XMLCite \textit{G. Ascione} et al., Proc. R. Soc. Edinb., Sect. A, Math. 152, No. 4, 1032--1057 (2022; Zbl 1500.60020) Full Text: DOI arXiv
Ascione, Giacomo; Leonenko, Nikolai; Pirozzi, Enrica Non-local solvable birth-death processes. (English) Zbl 1498.60336 J. Theor. Probab. 35, No. 2, 1284-1323 (2022). MSC: 60J80 60K25 33C45 60G22 PDFBibTeX XMLCite \textit{G. Ascione} et al., J. Theor. Probab. 35, No. 2, 1284--1323 (2022; Zbl 1498.60336) Full Text: DOI arXiv
Ketelbuters, John-John; Hainaut, Donatien CDS pricing with fractional Hawkes processes. (English) Zbl 1490.91237 Eur. J. Oper. Res. 297, No. 3, 1139-1150 (2022). MSC: 91G50 35R11 60G22 91G40 91G60 PDFBibTeX XMLCite \textit{J.-J. Ketelbuters} and \textit{D. Hainaut}, Eur. J. Oper. Res. 297, No. 3, 1139--1150 (2022; Zbl 1490.91237) Full Text: DOI Link
Patie, P.; Srapionyan, A. Spectral projections correlation structure for short-to-long range dependent processes. (English) Zbl 1499.60107 Eur. J. Appl. Math. 32, No. 1, 1-31 (2021). MSC: 60G07 47B40 62H20 62M02 62M07 PDFBibTeX XMLCite \textit{P. Patie} and \textit{A. Srapionyan}, Eur. J. Appl. Math. 32, No. 1, 1--31 (2021; Zbl 1499.60107) Full Text: DOI arXiv
Kolokoltsov, V. N.; Troeva, M. S. Fractional McKean-Vlasov and Hamilton-Jacobi-Bellman-Isaacs equations. (English. Russian original) Zbl 1491.35434 Proc. Steklov Inst. Math. 315, Suppl. 1, S165-S177 (2021); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 27, No. 3, 87-100 (2021). MSC: 35R11 35F21 60H15 PDFBibTeX XMLCite \textit{V. N. Kolokoltsov} and \textit{M. S. Troeva}, Proc. Steklov Inst. Math. 315, S165--S177 (2021; Zbl 1491.35434); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 27, No. 3, 87--100 (2021) Full Text: DOI
Kolokoltsov, V. N.; Troeva, M. S. Abstract McKean-Vlasov and Hamilton-Jacobi-Bellman equations, their fractional versions and related forward-backward systems on Riemannian manifolds. (English. Russian original) Zbl 1486.35436 Proc. Steklov Inst. Math. 315, 118-139 (2021); translation from Tr. Mat. Inst. Steklova 315, 128-150 (2021). MSC: 35R11 35F21 35R01 47D06 49L12 49N80 PDFBibTeX XMLCite \textit{V. N. Kolokoltsov} and \textit{M. S. Troeva}, Proc. Steklov Inst. Math. 315, 118--139 (2021; Zbl 1486.35436); translation from Tr. Mat. Inst. Steklova 315, 128--150 (2021) Full Text: DOI arXiv
Ascione, G.; Mishura, Yu.; Pirozzi, E. Convergence results for the time-changed fractional Ornstein-Uhlenbeck processes. (English) Zbl 1470.60111 Theory Probab. Math. Stat. 104, 23-47 (2021). MSC: 60G22 60F17 35R11 PDFBibTeX XMLCite \textit{G. Ascione} et al., Theory Probab. Math. Stat. 104, 23--47 (2021; Zbl 1470.60111) Full Text: DOI arXiv
Ascione, Giacomo; Leonenko, Nikolai; Pirozzi, Enrica Time-non-local Pearson diffusions. (English) Zbl 1467.35332 J. Stat. Phys. 183, No. 3, Paper No. 48, 42 p. (2021). MSC: 35R11 60K15 60J60 PDFBibTeX XMLCite \textit{G. Ascione} et al., J. Stat. Phys. 183, No. 3, Paper No. 48, 42 p. (2021; Zbl 1467.35332) Full Text: DOI arXiv
Hainaut, Donatien A fractional multi-states model for insurance. (English) Zbl 1466.91260 Insur. Math. Econ. 98, 120-132 (2021). MSC: 91G05 60J28 60K15 PDFBibTeX XMLCite \textit{D. Hainaut}, Insur. Math. Econ. 98, 120--132 (2021; Zbl 1466.91260) Full Text: DOI Link
Ascione, Giacomo; Leonenko, Nikolai; Pirozzi, Enrica Fractional immigration-death processes. (English) Zbl 1469.60277 J. Math. Anal. Appl. 495, No. 2, Article ID 124768, 27 p. (2021). MSC: 60J85 35Q92 92D25 PDFBibTeX XMLCite \textit{G. Ascione} et al., J. Math. Anal. Appl. 495, No. 2, Article ID 124768, 27 p. (2021; Zbl 1469.60277) Full Text: DOI arXiv
Hainaut, Donatien; Leonenko, Nikolai Option pricing in illiquid markets: a fractional jump-diffusion approach. (English) Zbl 1447.91174 J. Comput. Appl. Math. 381, Article ID 112995, 18 p. (2021). MSC: 91G20 26A33 60J74 PDFBibTeX XMLCite \textit{D. Hainaut} and \textit{N. Leonenko}, J. Comput. Appl. Math. 381, Article ID 112995, 18 p. (2021; Zbl 1447.91174) Full Text: DOI Link
Hainaut, Donatien Fractional Hawkes processes. (English) Zbl 07572687 Physica A 549, Article ID 124330, 20 p. (2020). MSC: 82-XX PDFBibTeX XMLCite \textit{D. Hainaut}, Physica A 549, Article ID 124330, 20 p. (2020; Zbl 07572687) Full Text: DOI Link
Leonenko, Nikolai N.; Papić, Ivan Correlation properties of continuous-time autoregressive processes delayed by the inverse of the stable subordinator. (English) Zbl 07529944 Commun. Stat., Theory Methods 49, No. 20, 5091-5113 (2020). MSC: 37M10 62M10 60G51 62-XX PDFBibTeX XMLCite \textit{N. N. Leonenko} and \textit{I. Papić}, Commun. Stat., Theory Methods 49, No. 20, 5091--5113 (2020; Zbl 07529944) Full Text: DOI Link
Beghin, Luisa; Caputo, Michele Commutative and associative properties of the Caputo fractional derivative and its generalizing convolution operator. (English) Zbl 1451.26007 Commun. Nonlinear Sci. Numer. Simul. 89, Article ID 105338, 6 p. (2020). Reviewer: Kai Diethelm (Schweinfurt) MSC: 26A33 26A06 60G51 PDFBibTeX XMLCite \textit{L. Beghin} and \textit{M. Caputo}, Commun. Nonlinear Sci. Numer. Simul. 89, Article ID 105338, 6 p. (2020; Zbl 1451.26007) Full Text: DOI
Ascione, Giacomo; Mishura, Yuliya; Pirozzi, Enrica Time-changed fractional Ornstein-Uhlenbeck process. (English) Zbl 1450.60030 Fract. Calc. Appl. Anal. 23, No. 2, 450-483 (2020). MSC: 60G22 26A33 35Q84 42A38 42B10 60H10 82C31 PDFBibTeX XMLCite \textit{G. Ascione} et al., Fract. Calc. Appl. Anal. 23, No. 2, 450--483 (2020; Zbl 1450.60030) Full Text: DOI arXiv
Leonenko, N. N.; Papić, I.; Sikorskii, A.; Šuvak, N. Approximation of heavy-tailed fractional Pearson diffusions in Skorokhod topology. (English) Zbl 1451.60037 J. Math. Anal. Appl. 486, No. 2, Article ID 123934, 21 p. (2020). MSC: 60F17 60J60 60K50 PDFBibTeX XMLCite \textit{N. N. Leonenko} et al., J. Math. Anal. Appl. 486, No. 2, Article ID 123934, 21 p. (2020; Zbl 1451.60037) Full Text: DOI Link
Kolokol’tsov, V. N. Mixed fractional differential equations and generalized operator-valued Mittag-Leffler functions. (English. Russian original) Zbl 1439.35538 Math. Notes 106, No. 5, 740-756 (2019); translation from Mat. Zametki 106, No. 5, 687-707 (2019). MSC: 35R11 33E12 PDFBibTeX XMLCite \textit{V. N. Kolokol'tsov}, Math. Notes 106, No. 5, 740--756 (2019; Zbl 1439.35538); translation from Mat. Zametki 106, No. 5, 687--707 (2019) Full Text: DOI
Kolokoltsov, Vassili N. The probabilistic point of view on the generalized fractional partial differential equations. (English) Zbl 1483.35002 Fract. Calc. Appl. Anal. 22, No. 3, 543-600 (2019). MSC: 35-02 35R11 35S05 35S15 60J25 60J35 60J50 PDFBibTeX XMLCite \textit{V. N. Kolokoltsov}, Fract. Calc. Appl. Anal. 22, No. 3, 543--600 (2019; Zbl 1483.35002) Full Text: DOI
Beghin, Luisa Long-memory Gaussian processes governed by generalized Fokker-Planck equations. (English) Zbl 1488.60081 ALEA, Lat. Am. J. Probab. Math. Stat. 16, No. 1, 439-461 (2019). MSC: 60G15 60G22 34A08 33C60 PDFBibTeX XMLCite \textit{L. Beghin}, ALEA, Lat. Am. J. Probab. Math. Stat. 16, No. 1, 439--461 (2019; Zbl 1488.60081) Full Text: arXiv Link
Mishura, Yuliya; Yurchenko-Tytarenko, Anton Fractional Cox-Ingersoll-Ross process with small Hurst indices. (English) Zbl 1454.60053 Mod. Stoch., Theory Appl. 6, No. 1, 13-39 (2019). Reviewer: David Nualart (Lawrence) MSC: 60G22 60H05 60H10 PDFBibTeX XMLCite \textit{Y. Mishura} and \textit{A. Yurchenko-Tytarenko}, Mod. Stoch., Theory Appl. 6, No. 1, 13--39 (2018; Zbl 1454.60053) Full Text: DOI arXiv
Mishura, Yu. S.; Piterbarg, V. I.; Ralchenko, K. V.; Yurchenko-Tytarenko, A. Yu. Stochastic representation and path properties of a fractional Cox-Ingersoll-Ross process. (English. Ukrainian original) Zbl 1409.60061 Theory Probab. Math. Stat. 97, 167-182 (2018); translation from Teor. Jmovirn. Mat. Stat. 97, 157-170 (2017). MSC: 60G22 60G15 60H10 PDFBibTeX XMLCite \textit{Yu. S. Mishura} et al., Theory Probab. Math. Stat. 97, 167--182 (2018; Zbl 1409.60061); translation from Teor. Jmovirn. Mat. Stat. 97, 157--170 (2017) Full Text: DOI arXiv
Mishura, Yuliya; Yurchenko-Tytarenko, Anton Fractional Cox-Ingersoll-Ross process with non-zero “mean”. (English) Zbl 1391.60078 Mod. Stoch., Theory Appl. 5, No. 1, 99-111 (2018). MSC: 60G22 60H05 60H10 PDFBibTeX XMLCite \textit{Y. Mishura} and \textit{A. Yurchenko-Tytarenko}, Mod. Stoch., Theory Appl. 5, No. 1, 99--111 (2018; Zbl 1391.60078) Full Text: DOI arXiv
Anh, V. V.; Leonenko, N. N.; Sikorskii, A. Stochastic representation of fractional Bessel-Riesz motion. (English) Zbl 1374.35415 Chaos Solitons Fractals 102, 135-139 (2017). MSC: 35R11 35R60 60H15 60G51 PDFBibTeX XMLCite \textit{V. V. Anh} et al., Chaos Solitons Fractals 102, 135--139 (2017; Zbl 1374.35415) Full Text: DOI Link
Leonenko, N. N.; Papić, I.; Sikorskii, A.; Šuvak, N. Heavy-tailed fractional Pearson diffusions. (English) Zbl 1373.33007 Stochastic Processes Appl. 127, No. 11, 3512-3535 (2017). MSC: 33C05 33C47 35P10 60G22 PDFBibTeX XMLCite \textit{N. N. Leonenko} et al., Stochastic Processes Appl. 127, No. 11, 3512--3535 (2017; Zbl 1373.33007) Full Text: DOI arXiv Link
Leonenko, Nikolai; Scalas, Enrico; Trinh, Mailan The fractional non-homogeneous Poisson process. (English) Zbl 1416.60054 Stat. Probab. Lett. 120, 147-156 (2017). MSC: 60G55 60G22 PDFBibTeX XMLCite \textit{N. Leonenko} et al., Stat. Probab. Lett. 120, 147--156 (2017; Zbl 1416.60054) Full Text: DOI arXiv Link
Gajda, Janusz; Wyłomańska, Agnieszka; Zimroz, Radosław Subordinated continuous-time AR processes and their application to modeling behavior of mechanical system. (English) Zbl 1400.60071 Physica A 464, 123-137 (2016). MSC: 60G52 62M10 PDFBibTeX XMLCite \textit{J. Gajda} et al., Physica A 464, 123--137 (2016; Zbl 1400.60071) Full Text: DOI
Wyłomańska, Agnieszka; Gajda, Janusz Stable continuous-time autoregressive process driven by stable subordinator. (English) Zbl 1400.60108 Physica A 444, 1012-1026 (2016). MSC: 60J75 62M09 PDFBibTeX XMLCite \textit{A. Wyłomańska} and \textit{J. Gajda}, Physica A 444, 1012--1026 (2016; Zbl 1400.60108) Full Text: DOI
Klimek, Małgorzata; Malinowska, Agnieszka B.; Odzijewicz, Tatiana Applications of the fractional Sturm-Liouville problem to the space-time fractional diffusion in a finite domain. (English) Zbl 1381.34017 Fract. Calc. Appl. Anal. 19, No. 2, 516-550 (2016). MSC: 34A08 34B24 35R11 47A75 PDFBibTeX XMLCite \textit{M. Klimek} et al., Fract. Calc. Appl. Anal. 19, No. 2, 516--550 (2016; Zbl 1381.34017) Full Text: DOI
Leonenko, Nikolai; Merzbach, Ely Fractional Poisson fields. (English) Zbl 1310.60035 Methodol. Comput. Appl. Probab. 17, No. 1, 155-168 (2015). MSC: 60G22 60G55 60G60 PDFBibTeX XMLCite \textit{N. Leonenko} and \textit{E. Merzbach}, Methodol. Comput. Appl. Probab. 17, No. 1, 155--168 (2015; Zbl 1310.60035) Full Text: DOI
Toaldo, Bruno Convolution-type derivatives, hitting-times of subordinators and time-changed \(C_0\)-semigroups. (English) Zbl 1315.60050 Potential Anal. 42, No. 1, 115-140 (2015). Reviewer: Ze-Chun Hu (Nanjing) MSC: 60G51 60J35 34K30 47D06 47G20 PDFBibTeX XMLCite \textit{B. Toaldo}, Potential Anal. 42, No. 1, 115--140 (2015; Zbl 1315.60050) Full Text: DOI arXiv
D’Ovidio, Mirko; Nane, Erkan Time dependent random fields on spherical non-homogeneous surfaces. (English) Zbl 1310.60060 Stochastic Processes Appl. 124, No. 6, 2098-2131 (2014). MSC: 60G60 60J60 60J65 PDFBibTeX XMLCite \textit{M. D'Ovidio} and \textit{E. Nane}, Stochastic Processes Appl. 124, No. 6, 2098--2131 (2014; Zbl 1310.60060) Full Text: DOI arXiv
Mijena, Jebessa B.; Nane, Erkan Correlation structure of time-changed Pearson diffusions. (English) Zbl 1296.60216 Stat. Probab. Lett. 90, 68-77 (2014). MSC: 60J60 PDFBibTeX XMLCite \textit{J. B. Mijena} and \textit{E. Nane}, Stat. Probab. Lett. 90, 68--77 (2014; Zbl 1296.60216) Full Text: DOI arXiv