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2021
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Alexander Sakhanenko, Vitali Wachtel, Evgeny Prokopenko and Anastasiya Shelepova
On the asymptotics of the distribution of the exit time beyond a non-increasing boundary for a compound renewal process
Siberian Electronic Mathematical Reports-sibirskie Elektronnye Matematicheskie Izvestiya 18, 9-26 (2021)
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Denis Denisov, Elena Perfilev and Vitali Wachtel
Tail asymptotics for the area under the excursion of a random walk with heavy-tailed increments
Journal of Applied Probability 58, 217-237 (2021)
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2020
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Dmitry Ioffe, Sébastien Ott, Yvan Velenik and Vitali Wachtel
Invariance principle for a potts interface along a wall
Journal of Statistical Physics , (in print)
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Denis Denisov, Dmitry Korshunov and Vitali Wachtel
Renewal theory for transient Markov chains with asymptotically zero drift
Transactions of the American Mathematical Society 373, 7253-7286 (2020)
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2019
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Denis Denisov and Vitali Wachtel
Alternative constructions of a harmonic function for a random walk in a cone
Electronic Journal of Probability 24, 92 (2019)
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Pietro Caputo, Dmitry Ioffe and Vitali Wachtel
Confinement of Brownian polymers under geometric area tilts
Electronic Journal of Probability 24, 37 (2019)
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Denis Denisov, Alexander Sakhanenko and Vitali Wachtel
First-passage times over moving boundaries for asymptotically stable walks
Theory of Probability & Its Applications 63, 613-633 (2019)
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Elena Perfilev and Vitali Wachtel
Local tail asymptotics for the joint distribution of length and of maximum of a random walk excursion
preprint, (2019)
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Denis Denisov, Dmitry A. Korshunov and Vitali Wachtel
Markov chains on Z(+): analysis of stationary measure via harmonic functions approach
Queueing Systems 91, 265-295 (2019)
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Denis Denisov, Dmitry Korshunov and Vitali Wachtel
Renewal theory for transient Markov chains with asymptotically zero drift
preprint, (2019)
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Pietro Caputo, Dmitry Ioffe and Vitali Wachtel
Tightness and line ensembles for Brownian polymers under geometric area tilts
preprint, (2019)
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2018
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Fiona Sloothaak, Vitali Wachtel and Bert Zwart
First-passage time asymptotics over moving boundaries for random walk bridges
Journal of Applied Probability 55, 627-651 (2018)
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Denis Denisov, Alexander Sakhanenko and Vitali Wachtel
First-passage times for random walks with nonidentically distributed increments
The Annals of Probability 46, 3313-3350 (2018)
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Elena Perfilev and Vitali Wachtel
Local asymptotics for the area under the random walk excursion
Advances in Applied Probability 50, 600-620 (2018)
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Vladimir Alekseevich Vatutin and Vitali Wachtel
Multi-type subcritical branching processes in a random environment
Advances in Applied Probability 50, 281-289 (2018)
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Günter Hinrichs, Martin Kolb and Vitali Wachtel
Persistence of one-dimensional AR(1)-sequences
preprint, (2018)
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2017
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Dmitry Ioffe, Yvan Velenik and Vitali Wachtel
Dyson Ferrari–Spohn diffusions and ordered walks under area tilts
Probability Theory and Related Fields 170, 11-47 (2017)
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Lothar Heinrich, Friedrich Pukelsheim and Vitali Wachtel
The variance of the discrepancy distribution of rounding procedures, and sums of uniform random variables
Metrika 80, 363-375 (2017)
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2016
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Vitali Wachtel and Denis Denisov
An exact asymptotics for the moment of crossing a curved boundary by an asymptotically stable random walk
Theory of Probability & Its Applications 60, 481-500 (2016)
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Denis Denisov, Dmitry A. Korshunov and Vitali Wachtel
At the Edge of Criticality: Markov Chains with Asymptotically Zero Drift
preprint, (2016)
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Leonid Mytnik and Vitali Wachtel
Regularity and irregularity of superprocesses with (1+β)-stable branching mechanism
(Springer briefs in probability and mathematical statistics) (Springer: Cham, Switzerland, 2016)
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Lothar Heinrich, Friedrich Pukelsheim and Vitali Wachtel
The Variance of the Discrepancy Distribution of Rounding Procedures, and Sums of Uniform Random Variables
preprint, (2016)
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Denis Denisov and Vitali Wachtel
Universality of local times of killed and reflected random walks
Electronic Communication in Probability 21, 1-11 (2016)
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2015
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Denis Denisov and Vitali Wachtel
Exit times for integrated random walks
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 51, 167-193 (2015)
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Jetlir Duraj and Vitali Wachtel
Invariance principles for random walks in cones
preprint, (2015)
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Denis Denisov, Martin Kolb and Vitali Wachtel
Local asymptotics for the area of random walk excursions
Journal of the London Mathematical Society 91, 495-513 (2015)
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Leonid Mytnik and Vitali Wachtel
Multifractal analysis of superprocesses with stable branching in dimension one
The Annals of Probability 43, 2763-2809 (2015)
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Denis Denisov and Vitali Wachtel
Random walks in cones
The Annals of Probability 43, 992-1044 (2015)
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2014
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Denis Denisov, Vladimir Alekseevich Vatutin and Vitali Wachtel
Local probabilities for random walks with negative drift conditioned to stay nonnegative
Electronic Journal of Probability 19, 88 (2014)
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2013
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Denis Denisov, Dmitry A. Korshunov and Vitali Wachtel
Potential analysis for positive recurrent Markov chains with asymptotically zero drift: Power-type asymptotics
Stochastic Processes and their Applications 123, 3027-3051 (2013)
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Vitali Wachtel, D. E. Denisov and Dmitry A. Korshunov
Tail asymptotics for the supercritical Galton-Watson process in the heavy-tailed case
Proceedings of the Steklov Institute of Mathematics 282, 273-297 (2013)
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Johannes Kugler and Vitali Wachtel
Upper Bounds for the Maximum of a Random Walk with Negative Drift
Journal of Applied Probability 50, 1131-1146 (2013)
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2012
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Denis Denisov and Vitali Wachtel
Martingale approach to subexponential asymptotics for random walks
Electronic Communications in Probability 17, 6 (2012)
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Denis Denisov and Vitali Wachtel
Ordered random walks with heavy tails
Electronic Journal of Probability 17, 4 (2012)
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2011
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S. Shneer and Vitali Wachtel
A unified approach to the heavy-traffic analysis of the maximum of random walks
Theory of Probability & Its Applications 55, 332-341 (2011)
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Published in Russian as: Общий подход к анализу максимума случайного блуждания в условиях тяжелой нагрузки. IN: Teoriya Veroyatnostei i ee Primeneniya, 55, 2, S. 335-343, https://doi.org/10.4213/tvp4203
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Klaus Fleischmann, Leonid Mytnik and Vitali Wachtel
Properties of States of Super-α-Stable Motion with Branching of Index 1 + β
in: Probability in Complex Physical Systems: In Honour of Erwin Bolthausen and Jürgen Gärtner, ed. by Jean-Dominique Deuschel, Barbara Gentz, Wolfgang König, Max von Renesse, Michael Scheutzow and Uwe Schmock, (Springer Proceedings in Mathematics; 11) 409-421 (Springer Berlin Heidelberg: Berlin, Heidelberg, 2011)
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2010
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Denis Denisov and Vitali Wachtel
Conditional limit theorems for ordered random walks
Electronic Journal of Probability 15, 292-322 (2010)
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Klaus Fleischmann, Leonid Mytnik and Vitali Wachtel
Hölder Index at a Given Point for Density States of Super-α-Stable Motion of Index 1+β
Journal of Theoretical Probability 24, 66-92 (2010)
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Vitali Wachtel
Local limit theorem for the maximum of asymptotically stable random walks
Probability Theory and Related Fields 152, 407-424 (2010)
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Klaus Fleischmann, Leonid Mytnik and Vitali Wachtel
Optimal local Hölder index for density states of superprocesses with (1+ β)-branching mechanism
The Annals of Probability 38, 1180-1220 (2010)
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Vladimir Alekseevich Vatutin and Vitali Wachtel
Sudden extinction of a critical branching process in a random environment
Theory of Probability & Its Applications 54, 466-484 (2010)
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Published in Russian as: Внезапное вырождение критического ветвящегося процесса в случайной среде. IN: Teoriya Veroyatnostei i ee Primeneniya, 54, 3, S. 417-438, https://doi.org/10.4213/tvp2803
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Nina Gantert, Peter Mörters and Vitali Wachtel
Trap models with vanishing drift: scaling limits and ageing regimes
ALEA: Latin American Journal of Probability and Mathematical Statistics 7, 477-501 (2010)
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2009
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Klaus Fleischmann and Vitali Wachtel
On the left tail asymptotics for the limit law of supercritical Galton–Watson processes in the Böttcher case
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 45, 201-225 (2009)
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Vitali Wachtel
Transition phenomena for ladder epochs of random walks with small negative drift
Advances in Applied Probability 41, 1189-1214 (2009)
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2008
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Vladimir Alekseevich Vatutin, Vitali Wachtel and Klaus Fleischmann
Critical Galton–Watson processes: the maximum of total progenies within a large window
Theory of Probability & Its Applications 52, 470-492 (2008)
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Published in Russian as: Критические процессы Гальтона - Ватсона: Максимум общего числа частиц внутри большого окна. IN: Teoriya Veroyatnostei i ee Primeneniya, 52, 3, S. 419-445, https://doi.org/10.4213/tvp72
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Vitali Wachtel
Limit theorems for probabilities of large deviations of a critical Galton–Watson process having power tails
Theory of Probability & Its Applications 52, 674-688 (2008)
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Published in Russian as: Предельные теоремы для вероятностей больших уклонений критического процесса Гальтона - Ватсона со степенными хвостами. IN: Teoriya Veroyatnostei i ee Primeneniya, 52, 4, S. 644-659, https://doi.org/10.4213/tvp1527
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Vladimir Alekseevich Vatutin and Vitali Wachtel
Local probabilities for random walks conditioned to stay positive
Probability Theory and Related Fields 143, 177-217 (2008)
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Klaus Fleischmann, Peter Mörters and Vitali Wachtel
Moderate deviations for a random walk in random scenery
Stochastic Processes and their Applications 118, 1768-1802 (2008)
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S. V. Nagaev and V. I. Vachtel
On sums of independent random variables without power moments
Siberian Mathematical Journal 49, 1091-1100 (2008)
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2007
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Klaus Fleischmann and Vitali Wachtel
Large deviations for sums indexed by the generations of a Galton–Watson process
Probability Theory and Related Fields 141, 445-470 (2007)
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Klaus Fleischmann and Vitali Wachtel
Lower deviation probabilities for supercritical Galton–Watson processes
Annales de l'Institut Henri Poincare (B) Probability and Statistics 43, 233-255 (2007)
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S. V. Nagaev and Vitali Wachtel
The Critical Galton-Watson Process Without Further Power Moments
Journal of Applied Probability 44, 753-769 (2007)
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2006
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Klaus Fleischmann, Peter Mörters and Vitali Wachtel
Hydrodynamic limit fluctuations of super-Brownian motion with a stable catalyst
Electronic Journal of Probability 11, 723-767 (2006)
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Klaus Fleischmann and Vitali Wachtel
Large scale localization of a spatial version of Neveu’s branching process
Stochastic Processes and their Applications 116, 983-1011 (2006)
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S. V. Nagaev and Vitali Wachtel
On sums of independent random variables without power moments
Doklady Mathematics 74, 683-685 (2006)
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S. V. Nagaev and Vitali Wachtel
On the local limit theorem for a critical Galton–Watson process
Theory of Probability & Its Applications 50, 400-419 (2006)
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Published in Russian as: О локальной предельной теореме для критического процесса Гальтона - Ватсона. IN: Teoriya Veroyatnostei i ee Primeneniya, 50, 3, S. 457-479, https://doi.org/10.4213/tvp89
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S. V. Nagaev and Vitali Wachtel
Probability inequalities for a critical Galton-Watson process
Theory of Probability & Its Applications 50, 225-247 (2006)
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Published in Russian as: Вероятностные неравенства для критического процесса Гальтона - Ватсона. IN: Teoriya Veroyatnostei i ee Primeneniya, 50, 2, S. 266-291, https://doi.org/10.4213/tvp107
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2003
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S. V. Nagaev and Vitali Wachtel
Limit theorems for probabilities of large deviations of a Galton–Watson process
Discrete Mathematics and Applications 13, 1-26 (2003)
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Published in Russian as: Предельные теоремы для вероятностей больших уклонений процесса Гальтона - Ватсона. IN: Diskretnaya Matematika, 15, 1, S. 3-27, https://doi.org/10.4213/dm183
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1999
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S. V. Nagaev, L. V. Nedorezov and Vitali Wachtel
Вероятностная непрерывно-дискретная модель динамики численности изолированной популяции [ = A probabilistic continuous-discrete model of the dynamics of the size of an isolated population]
Sibirskiĭ Zhurnal Industrialʹnoĭ Matematiki 2, 147-152 (1999)
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