Duraj, Jetlir; Raschel, Kilian; Tarrago, Pierre; Wachtel, Vitali Martin boundary of random walks in convex cones. (Frontière de Martin de marches aléatoires dans des cônes convexes.) (English. French summary) Zbl 1492.60123 Ann. Henri Lebesgue 5, 559-609 (2022). MSC: 60G50 60G40 60F17 PDFBibTeX XMLCite \textit{J. Duraj} et al., Ann. Henri Lebesgue 5, 559--609 (2022; Zbl 1492.60123) Full Text: DOI arXiv
Denisov, Denis E.; Hinrichs, Günter; Sakhanenko, Alexander I.; Wachtel, Vitali I. Crossing an asymptotically square-root boundary by the Brownian motion. (English. Russian original) Zbl 1495.60076 Proc. Steklov Inst. Math. 316, 105-120 (2022); translation from Tr. Mat. Inst. Steklova 316, 113-128 (2022). Reviewer: Anatoliy Swishchuk (Calgary) MSC: 60J65 60G40 PDFBibTeX XMLCite \textit{D. E. Denisov} et al., Proc. Steklov Inst. Math. 316, 105--120 (2022; Zbl 1495.60076); translation from Tr. Mat. Inst. Steklova 316, 113--128 (2022) Full Text: DOI
Denisov, Denis; Sakhanenko, Alexander; Wachtel, Vitali First-passage times for random walks in the triangular array setting. (English) Zbl 1496.60041 Chaumont, Loïc (ed.) et al., A lifetime of excursions through random walks and Lévy processes. A volume in honour of Ron Doney’s 80th birthday. Cham: Birkhäuser. Prog. Probab. 78, 181-203 (2021). MSC: 60G50 60F17 60G40 PDFBibTeX XMLCite \textit{D. Denisov} et al., Prog. Probab. 78, 181--203 (2021; Zbl 1496.60041) Full Text: DOI arXiv
Sakhanenko, A. I.; Wachtel, V. I.; Prokopenko, E. I.; Shelepova, A. D. On the asymptotics of the distribution of the exit time beyond a non-increasing boundary for a compound renewal process. (Russian. English summary) Zbl 1455.60122 Sib. Èlektron. Mat. Izv. 18, No. 1, 9-26 (2021). MSC: 60K15 60F17 PDFBibTeX XMLCite \textit{A. I. Sakhanenko} et al., Sib. Èlektron. Mat. Izv. 18, No. 1, 9--26 (2021; Zbl 1455.60122) Full Text: DOI
Aurzada, Frank (ed.); Kolb, Martin (ed.); Pène, Francoise (ed.); Wachtel, Vitali (ed.) Stochastic processes under constraints. Abstracts from the workshop held September 27 – October 3, 2020 (hybrid meeting). (English) Zbl 1473.00038 Oberwolfach Rep. 17, No. 4, 1601-1656 (2020). MSC: 00B05 00B25 60-06 60Gxx 60F10 60F17 PDFBibTeX XMLCite \textit{F. Aurzada} (ed.) et al., Oberwolfach Rep. 17, No. 4, 1601--1656 (2020; Zbl 1473.00038) Full Text: DOI
Denisov, Denis; Korshunov, Dmitry; Wachtel, Vitali Renewal theory for transient Markov chains with asymptotically zero drift. (English) Zbl 1454.60136 Trans. Am. Math. Soc. 373, No. 10, 7253-7286 (2020). MSC: 60K05 60J05 60G42 PDFBibTeX XMLCite \textit{D. Denisov} et al., Trans. Am. Math. Soc. 373, No. 10, 7253--7286 (2020; Zbl 1454.60136) Full Text: DOI arXiv Link
Duraj, Jetlir; Wachtel, Vitali Invariance principles for random walks in cones. (English) Zbl 1456.60103 Stochastic Processes Appl. 130, No. 7, 3920-3942 (2020). MSC: 60G50 60G40 60F17 PDFBibTeX XMLCite \textit{J. Duraj} and \textit{V. Wachtel}, Stochastic Processes Appl. 130, No. 7, 3920--3942 (2020; Zbl 1456.60103) Full Text: DOI arXiv
Hinrichs, Günter; Kolb, Martin; Wachtel, Vitali Persistence of one-dimensional AR(1)-sequences. (English) Zbl 1431.60070 J. Theor. Probab. 33, No. 1, 65-102 (2020). MSC: 60J05 60G40 PDFBibTeX XMLCite \textit{G. Hinrichs} et al., J. Theor. Probab. 33, No. 1, 65--102 (2020; Zbl 1431.60070) Full Text: DOI arXiv
Denisov, Denis; Korshunov, Dmitry; Wachtel, Vitali Markov chains on \({{\mathbb{Z}}^+}\): analysis of stationary measure via harmonic functions approach. (English) Zbl 1466.60142 Queueing Syst. 91, No. 3-4, 265-295 (2019). MSC: 60J10 60J45 60K25 60F10 31C05 PDFBibTeX XMLCite \textit{D. Denisov} et al., Queueing Syst. 91, No. 3--4, 265--295 (2019; Zbl 1466.60142) Full Text: DOI
Denisov, D.; Sakhanenko, A.; Wachtel, V. First-passage times over moving boundaries for asymptotically stable walks. (English. Russian original) Zbl 1442.60049 Theory Probab. Appl. 63, No. 4, 613-633 (2019); translation from Teor. Veroyatn. Primen. 63, No. 4, 755-778 (2018). MSC: 60G50 60F17 60G51 60G52 PDFBibTeX XMLCite \textit{D. Denisov} et al., Theory Probab. Appl. 63, No. 4, 613--633 (2019; Zbl 1442.60049); translation from Teor. Veroyatn. Primen. 63, No. 4, 755--778 (2018) Full Text: DOI arXiv
Vatutin, Vladimir; Wachtel, Vitali Multi-type subcritical branching processes in a random environment. (English) Zbl 1431.60103 Adv. Appl. Probab. 50, No. A, 281-289 (2018). MSC: 60J80 60F99 PDFBibTeX XMLCite \textit{V. Vatutin} and \textit{V. Wachtel}, Adv. Appl. Probab. 50, No. A, 281--289 (2018; Zbl 1431.60103) Full Text: DOI arXiv
Denisov, Denis; Sakhanenko, Alexander; Wachtel, Vitali First-passage times for random walks with nonidentically distributed increments. (English) Zbl 1434.60126 Ann. Probab. 46, No. 6, 3313-3350 (2018). Reviewer: Alexander Iksanov (Kiev) MSC: 60G50 60G40 60F17 PDFBibTeX XMLCite \textit{D. Denisov} et al., Ann. Probab. 46, No. 6, 3313--3350 (2018; Zbl 1434.60126) Full Text: DOI arXiv Euclid
Sloothaak, Fiona; Wachtel, Vitali; Zwart, Bert First-passage time asymptotics over moving boundaries for random walk bridges. (English) Zbl 1401.60082 J. Appl. Probab. 55, No. 2, 627-651 (2018). MSC: 60G50 60F05 PDFBibTeX XMLCite \textit{F. Sloothaak} et al., J. Appl. Probab. 55, No. 2, 627--651 (2018; Zbl 1401.60082) Full Text: DOI arXiv
Wachtel, Vitali I.; Denisov, Denis E. An exact asymptotics for the moment of crossing a curved boundary by an asymptotically stable random walk. (English. Russian original) Zbl 1375.60088 Theory Probab. Appl. 60, No. 3, 481-500 (2016); translation from Teor. Veroyatn. Primen. 60, No. 3, 459-481 (2016). MSC: 60G50 62E15 60E05 PDFBibTeX XMLCite \textit{V. I. Wachtel} and \textit{D. E. Denisov}, Theory Probab. Appl. 60, No. 3, 481--500 (2016; Zbl 1375.60088); translation from Teor. Veroyatn. Primen. 60, No. 3, 459--481 (2016) Full Text: DOI arXiv
Denisov, Denis; Wachtel, Vitali Random walks in cones. (English) Zbl 1332.60066 Ann. Probab. 43, No. 3, 992-1044 (2015). Reviewer: Peter Kern (Düsseldorf) MSC: 60G50 60F05 60G40 60J45 PDFBibTeX XMLCite \textit{D. Denisov} and \textit{V. Wachtel}, Ann. Probab. 43, No. 3, 992--1044 (2015; Zbl 1332.60066) Full Text: DOI arXiv Euclid
Wachtel, V. I.; Denisov, D. E.; Korshunov, D. A. Tail asymptotics for the supercritical Galton-Watson process in the heavy-tailed case. (English. Russian original) Zbl 1290.60087 Proc. Steklov Inst. Math. 282, 273-297 (2013); translation from Tr. Mat. Inst. Steklova 282, 288-314 (2013). Reviewer: P. R. Parthasarathy (Chennai) MSC: 60J80 PDFBibTeX XMLCite \textit{V. I. Wachtel} et al., Proc. Steklov Inst. Math. 282, 273--297 (2013; Zbl 1290.60087); translation from Tr. Mat. Inst. Steklova 282, 288--314 (2013) Full Text: DOI arXiv
Kugler, Johannes; Wachtel, Vitali Upper bounds for the maximum of a random walk with negative drift. (English) Zbl 1293.60052 J. Appl. Probab. 50, No. 4, 1131-1146 (2013). MSC: 60G50 60G52 PDFBibTeX XMLCite \textit{J. Kugler} and \textit{V. Wachtel}, J. Appl. Probab. 50, No. 4, 1131--1146 (2013; Zbl 1293.60052) Full Text: DOI arXiv Euclid
Wachtel, Vitali Local limit theorem for the maximum of asymptotically stable random walks. (English) Zbl 1237.60039 Probab. Theory Relat. Fields 152, No. 3-4, 407-424 (2012). MSC: 60G50 60G52 60E07 60K05 PDFBibTeX XMLCite \textit{V. Wachtel}, Probab. Theory Relat. Fields 152, No. 3--4, 407--424 (2012; Zbl 1237.60039) Full Text: DOI Link
Fleischmann, Klaus; Mytnik, Leonid; Wachtel, Vitali Optimal local Hölder index for density states of superprocesses with \((1+\beta )\)-branching mechanism. (English) Zbl 1207.60055 Ann. Probab. 38, No. 3, 1180-1220 (2010). Reviewer: Isamu Dôku (Saitama) MSC: 60J68 60J80 60G57 PDFBibTeX XMLCite \textit{K. Fleischmann} et al., Ann. Probab. 38, No. 3, 1180--1220 (2010; Zbl 1207.60055) Full Text: DOI arXiv
Wachtel, Vitali Transition phenomena for ladder epochs of random walks with small negative drift. (English) Zbl 1205.60093 Adv. Appl. Probab. 41, No. 4, 1189-1214 (2009). Reviewer: Aleksander Iksanov (Kiev) MSC: 60G50 60G52 PDFBibTeX XMLCite \textit{V. Wachtel}, Adv. Appl. Probab. 41, No. 4, 1189--1214 (2009; Zbl 1205.60093) Full Text: DOI arXiv
Vatutin, Vladimir A.; Wachtel, Vitali Local probabilities for random walks conditioned to stay positive. (English) Zbl 1158.60014 Probab. Theory Relat. Fields 143, No. 1-2, 177-217 (2009). Reviewer: Rudolf Gorenflo (Berlin) MSC: 60G50 60G52 60E07 PDFBibTeX XMLCite \textit{V. A. Vatutin} and \textit{V. Wachtel}, Probab. Theory Relat. Fields 143, No. 1--2, 177--217 (2009; Zbl 1158.60014) Full Text: DOI arXiv
Fleischmann, Klaus; Mörters, Peter; Wachtel, Vitali Moderate deviations for a random walk in random scenery. (English) Zbl 1157.60020 Stochastic Processes Appl. 118, No. 10, 1768-1802 (2008). Reviewer: Alex V. Kolnogorov (Novgorod) MSC: 60F10 60K37 PDFBibTeX XMLCite \textit{K. Fleischmann} et al., Stochastic Processes Appl. 118, No. 10, 1768--1802 (2008; Zbl 1157.60020) Full Text: DOI arXiv
Fleischmann, Klaus; Wachtel, Vitali Large deviations for sums indexed by the generations of a Galton-Watson process. (English) Zbl 1141.60048 Probab. Theory Relat. Fields 141, No. 3-4, 445-470 (2008). MSC: 60J80 60F10 PDFBibTeX XMLCite \textit{K. Fleischmann} and \textit{V. Wachtel}, Probab. Theory Relat. Fields 141, No. 3--4, 445--470 (2008; Zbl 1141.60048) Full Text: DOI arXiv
Nagaev, S. V.; Wachtel, V. The critical Galton-Watson process without further power moments. (English) Zbl 1141.60049 J. Appl. Probab. 44, No. 3, 753-769 (2007). Reviewer: Heinrich Hering (Rockenberg) MSC: 60J80 60F05 PDFBibTeX XMLCite \textit{S. V. Nagaev} and \textit{V. Wachtel}, J. Appl. Probab. 44, No. 3, 753--769 (2007; Zbl 1141.60049) Full Text: DOI