Prof. Dr. Vitali Wachtel

Lebenslauf

 

Degrees
2000                 Master in Mathematics ,  Novosibirsk State University
2003                 PhD in Mathematics, Novosibirsk State University
2008                 Habilitation, Technische Universität München


Positions
2003-2007         Post-Doc, Weierstrass Institute, Berlin
2007-2008         Post-Doc, Technische Universität München
2008-2014         Akademischer Rat, University of Munich
since 2014         Professor, University of Augsburg    

 

 

 

 

Forschungsschwerpunkte

Austrittszeiten der Irrfahrten

Austrittszeiten der Irrfahrten spielen eine sehr wichtige Rolle in vielen stochastischen Modellen in der Physik, Finanzmathematik und Statistik. Am Lehrstuhl werden insbesondere Austrittsprobleme mit beweglichen Grenzen untersucht, die bei der Konstruktion von sequentiellen Prozeduren in Statistik von sehr großer Bedeutung sind. Außerdem werden die Austrittszeiten aus Kegeln von mehrdimensionalen Irrfahrten untersucht. Von besonderem Interesse sind die Grenzwertsätze für die auf Nichtaustreten bedingten Irrfahrten. Solche Aussagen finden zahlreiche Anwendungen in Kombinatorik.

 

Asymptotisches Verhalten von Markovketten

Seit der Arbeit von Lamperit in den 60er Jahren genießen die Markovketten mit asymptotisch verschwindendem Drift ständige Aufmerksamkeit von Stochastikern. Sehr intensiv wurde die Frage der Rekurrenz/Transparenz bearbeitet. Außerdem wurden etliche relativ grobe Abschätzungen für invariante Maße solcher Ketten hergeleitet. Das Hauptziel in diesem Projekt ist es, das präzise Tail-Verhalten von stationären Maßen zu klären. Dafür wird Potenzialtheorie benutzt.

 

 

 


 

Forschungsgebiete

  • Branching processes
  • Large deviations
  • Random media
  • Random walks
  • Markov chains

 

 

 

Publikationen

2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 | 2008 | 2007 | 2006 | 2003 | 1999

2022

Denis E. Denisov, Günter Hinrichs, Alexander I. Sakhanenko and Vitali I. Wachtel
Crossing an asymptotically square-root boundary by the Brownian motion

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2021

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

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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

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2020

Dmitry Ioffe, Sébastien Ott, Yvan Velenik and Vitali Wachtel
Invariance principle for a potts interface along a wall

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Günter Hinrichs, Martin Kolb and Vitali Wachtel
Persistence of one-dimensional AR(1)-sequences

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Denis Denisov, Dmitry Korshunov and Vitali Wachtel
Renewal theory for transient Markov chains with asymptotically zero drift

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2019

Denis Denisov and Vitali Wachtel
Alternative constructions of a harmonic function for a random walk in a cone

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Pietro Caputo, Dmitry Ioffe and Vitali Wachtel
Confinement of Brownian polymers under geometric area tilts

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Denis Denisov, Alexander Sakhanenko and Vitali Wachtel
First-passage times over moving boundaries for asymptotically stable walks

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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

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Denis Denisov, Dmitry A. Korshunov and Vitali Wachtel
Markov chains on Z(+): analysis of stationary measure via harmonic functions approach

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Pietro Caputo, Dmitry Ioffe and Vitali Wachtel
Tightness and line ensembles for Brownian polymers under geometric area tilts

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2018

Fiona Sloothaak, Vitali Wachtel and Bert Zwart
First-passage time asymptotics over moving boundaries for random walk bridges

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Denis Denisov, Alexander Sakhanenko and Vitali Wachtel
First-passage times for random walks with nonidentically distributed increments

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Elena Perfilev and Vitali Wachtel
Local asymptotics for the area under the random walk excursion

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Vladimir Alekseevich Vatutin and Vitali Wachtel
Multi-type subcritical branching processes in a random environment

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2017

Dmitry Ioffe, Yvan Velenik and Vitali Wachtel
Dyson Ferrari–Spohn diffusions and ordered walks under area tilts

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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

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2016

Vitali Wachtel and Denis Denisov
An exact asymptotics for the moment of crossing a curved boundary by an asymptotically stable random walk

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Denis Denisov, Dmitry A. Korshunov and Vitali Wachtel
At the Edge of Criticality: Markov Chains with Asymptotically Zero Drift

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Leonid Mytnik and Vitali Wachtel
Regularity and irregularity of superprocesses with (1+β)-stable branching mechanism

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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

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Denis Denisov and Vitali Wachtel
Universality of local times of killed and reflected random walks

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2015

Denis Denisov and Vitali Wachtel
Exit times for integrated random walks

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Jetlir Duraj and Vitali Wachtel
Invariance principles for random walks in cones

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Denis Denisov, Martin Kolb and Vitali Wachtel
Local asymptotics for the area of random walk excursions

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Leonid Mytnik and Vitali Wachtel
Multifractal analysis of superprocesses with stable branching in dimension one

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Denis Denisov and Vitali Wachtel
Random walks in cones

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2014

Denis Denisov, Vladimir Alekseevich Vatutin and Vitali Wachtel
Local probabilities for random walks with negative drift conditioned to stay nonnegative

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2013

Denis Denisov, Dmitry A. Korshunov and Vitali Wachtel
Potential analysis for positive recurrent Markov chains with asymptotically zero drift: power-type asymptotics

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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

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Johannes Kugler and Vitali Wachtel
Upper Bounds for the Maximum of a Random Walk with Negative Drift

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2012

Denis Denisov and Vitali Wachtel
Martingale approach to subexponential asymptotics for random walks

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Denis Denisov and Vitali Wachtel
Ordered random walks with heavy tails

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2011

S. Shneer and Vitali Wachtel
A unified approach to the heavy-traffic analysis of the maximum of random walks

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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

Klaus Fleischmann, Leonid Mytnik and Vitali Wachtel
Properties of states of super-α-stable motion with branching of index 1 + β

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2010

Denis Denisov and Vitali Wachtel
Conditional limit theorems for ordered random walks

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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

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Vitali Wachtel
Local limit theorem for the maximum of asymptotically stable random walks

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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

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Vladimir Alekseevich Vatutin and Vitali Wachtel
Sudden extinction of a critical branching process in a random environment

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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

Nina Gantert, Peter Mörters and Vitali Wachtel
Trap models with vanishing drift: scaling limits and ageing regimes

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2009

Klaus Fleischmann and Vitali Wachtel
On the left tail asymptotics for the limit law of supercritical Galton–Watson processes in the Böttcher case

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Vitali Wachtel
Transition phenomena for ladder epochs of random walks with small negative drift

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2008

Vladimir Alekseevich Vatutin, Vitali Wachtel and Klaus Fleischmann
Critical Galton–Watson processes: the maximum of total progenies within a large window

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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

Vitali Wachtel
Limit theorems for probabilities of large deviations of a critical Galton–Watson process having power tails

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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

Vladimir Alekseevich Vatutin and Vitali Wachtel
Local probabilities for random walks conditioned to stay positive

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Klaus Fleischmann, Peter Mörters and Vitali Wachtel
Moderate deviations for a random walk in random scenery

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S. V. Nagaev and V. I. Vachtel
On sums of independent random variables without power moments

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2007

Klaus Fleischmann and Vitali Wachtel
Large deviations for sums indexed by the generations of a Galton–Watson process

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Klaus Fleischmann and Vitali Wachtel
Lower deviation probabilities for supercritical Galton–Watson processes

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S. V. Nagaev and Vitali Wachtel
The Critical Galton-Watson Process Without Further Power Moments

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2006

Klaus Fleischmann, Peter Mörters and Vitali Wachtel
Hydrodynamic limit fluctuations of super-Brownian motion with a stable catalyst

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Klaus Fleischmann and Vitali Wachtel
Large scale localization of a spatial version of Neveu’s branching process

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S. V. Nagaev and Vitali Wachtel
On sums of independent random variables without power moments

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S. V. Nagaev and Vitali Wachtel
On the local limit theorem for a critical Galton–Watson process

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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

S. V. Nagaev and Vitali Wachtel
Probability inequalities for a critical Galton-Watson process

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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

2003

S. V. Nagaev and Vitali Wachtel
Limit theorems for probabilities of large deviations of a Galton–Watson process

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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

1999

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]

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