Prof. Dr. Ilya Pavlyukevich

Kurzbiographie

Berufstätigkeit

  • seit 2009: Professor (W2, seit 2018 W3) der Professur für Stochastik und Anwendungen in den Naturwissenschaften, Friedrich-Schiller-Universität Jena
  • 2008 - 2009: Gastprofessur für Wirtschaftmathematik, Fakultät für Mathematik, Naturwissenschaften, und Informatik, Brandenburgische Technische Universität Cottbus
  • April - August 2008: Lehrstuhlvertreter (W3), Mathematische Statistik, Institut für Angewandte Mathematik, Universität Heidelberg
  • 2007 - 2009: Wissenschaftlicher Mitarbeiter, SFB 555 "Complex Nonlinear Processes", Humboldt-Universität zu Berlin
  • 2004 - 2007: Wissenschaftlicher Mitarbeiter, DFG-Forschungsprojekt "Stochastic Dynamics of Climate States", Humboldt-Universität zu Berlin
  • März - Juli 2005: JSPS Post-Doctoral Fellow (with Prof. N. Yoshida), Graduate School of Mathematical Studies, University of Tokyo
  • 2003 - 2004: Wissenschaftlicher Mitarbeiter, DFG-Forschungszentrum "Mathematics for Key Technologies" (Matheon), Humboldt-Universität zu Berlin
  • 2001 - 2003: Wissenschaftliche Hilfskraft, Institut für Mathematik, Technischr Universität Berlin

Ausbildung

  • 1998 - 2001: Promotionsstudium in Mathematik, Graduiertenkolleg "Stochastic Processes and Probabilistic Analysis", Humboldt-Universität zu Berlin
  • 1991 - 1996: Grundständiges Studium in Mathematik, Department of Mechanics and Mathematics, Moscow State University (M. V. Lomonosov)
  • 1989 - 1991: Physics-Mathematics School No. 18 (A. N. Kolmogorov), Moscow State University

Forschung

Publikationen

Bücher

Artikel (geordnet nach Verfassungzeitpunkt)

  • I. Pavlyukevich and G. Shevchenko
    Stratonovich SDE with irregular coecients: Girsanov's example revisited
    submitted [arXiv]Externer Link
  • A. Kulik and I. Pavlyukevich
    Non-Gaussian limit theorem for non-linear Langevin equations driven by Lévy noise
    Annales de l'Institut Henri Poincaré, to appear
  • L.-S. Hartmann and I. Pavlyukevich
    Advection-diusion equation on a half-line with boundary Lévy noise
    Discrete and Continuous Dynamical Systems - Series B, 24(2), 637655, 2019
  • I. Kuhwald and I. Pavlyukevich
    Bistable behaviour of a jump-diffusion driven by a periodic stable-like additive process
    Dicsrete and Continuous Dynamical Systems - Series B, 21(9), 3175-3190, 2016
  • N. Lingala, N.S. Namachchivaya, I. Pavlyukevich
    Random perturbations of a periodically driven nonlinear oscillator: Escape from a resonance zone
    Nonlinearity, 30, 1376-1404, 2017
  • I. Kuhwald and I. Pavlyukevich
    Stochastic resonance with multiplicative heavy-tailed Lévy noise: Optimal tuning on an algebraic time scale
    Stochastics and Dynamics, 17(4), 1750027, 2017
  • N. Lingala, N.S. Namachchivaya, I. Pavlyukevich and W. Wedig
    Random perturbations of periodically driven nonlinear oscillators
    IUTAM Symposium on Analytical Methods in Nonlinear Dynamics, Procedia IUTAM, 19, 91-100, 2016
  • I. Kuhwald and I. Pavlyukevich
    Stochastic resonance in systems driven by α-stable Lévy noise
    Proceedings of the 12th International Conference on Vibration Problems ICOVP 2015, Procedia Engineering, 144, 1307-1314, 2016
  • I. Pavlyukevich, Y. Li, Y. Xu and A. Chechkin
    Directed transport induced by spatially modulated Lévy flights
    Journal of Physics A: Mathematical and Theoretical, 48:495004, 2015
  • T. Burghoff and I. Pavlyukevich
    Spectral analysis of a discrete metastable system driven by Lévy flights
    The Journal of Statistical Physics, 161(1), 171-196, 2015 [arXiv]Externer Link
  • A. Chechkin and I. Pavlyukevich
    Marcus versus Stratonovich for systems with jump noise
    Journal of Physics: A Mathematical and Theoretical, 47, 342001Externer Link, 2014 [arXiv]Externer Link
  • M. Högele and I. Pavlyukevich
    Metastability in a class of hyperbolic dynamical systems perturbed by heavy-tailed Lévy type noise
    Stochastics and Dynamics, 15(3), 1550019, 2015, [arXiv]Externer Link
  • I. Pavlyukevich and M. Riedle
    Non-standard Skorokhod convergence of Lévy-driven convolution integrals in Hilbert spaces
    The Journal of Stochastic Analysis and Applications, 33(2), 271-305, 2015 [arXiv]Externer Link
  • M. Högele and I. Pavlyukevich
    The exit problem from a neighborhood of the global attractor for dynamical systems perturbed by heavy-tailed Lévy processes
    The Journal of Stochastic Analysis and Applications, 32(1), 163-190Externer Link, 2014 [arXiv]Externer Link
  • R. Hintze and I. Pavlyukevich
    Small noise asymptotics of a Lévy flights driven displacement process
    Procedia IUTAM, 6, 204-210Externer Link, 2013
  • R. Hintze and I. Pavlyukevich
    Small noise asymptotics and first passage times of integrated Ornstein--Uhlenbeck processes driven by α-stable Lévy processes
    Bernoulli, 20(1), 265-281Externer Link, 2014 [arXiv]Externer Link
  • I. Pavlyukevich
    First exit times of solutions of stochastic differential equations driven by multiplicative Lévy noise with heavy tails
    Stochastics and Dynamics, 11(2&3), 495--519Externer Link, 2011 [arXiv]Externer Link
  • I. Pavlyukevich, B. Dybiec, A. Chechkin and I. M. Sokolov
    Lévy ratchet in a weak noise limit: Theory and simulation
    The European Physical Journal. Special Topics, 191, 223-237, 2010
  • P. Imkeller, I. Pavlyukevich and T. Wetzel
    The hierarchy of exit times of Lévy-driven Langevin equations
    The European Physical Journal. Special Topics, 191, 211-222, 2010
  • P. Imkeller, I. Pavlyukevich and M. Stauch
    First exit times of non-linear dynamical systems in ℝᵈ perturbed by multifractal Lévy noise
    The Journal of Statistical Physics 141 (1), 94-119, 2010
  • C. Hein, P. Imkeller and I. Pavlyukevich
    Limit theorems for p-variations of solutions of SDEs driven by additive stable Lévy noise and model selection for paleo-climatic data
    in J. Duan, S. Luo and C. Wang (eds.), Recent Development in Stochastic Dynamics and Stochastic Analysis, Interdisciplinary Math. Sciences 8, 137-150, 2009
  • S. Borovkova, F. J. Permana and I. Pavlyukevich
    Modeling electricity prices by potential Lévy diffusions
    The Journal of Energy Markets, 2(3), 83-110Externer Link, 2009
  • I. Pavlyukevich and I. M. Sokolov
    One-dimensional space-discrete transport subject to Lévy perturbations
    The Journal of Statistical Physics 133 (1), 205-215, 2008 [arXiv]Externer Link
  • P. Imkeller, I. Pavlyukevich and T. Wetzel
    First exit times for Lévy-driven diffusions with exponentially light jumps
    The Annals of Probability 37(2), 530-564, 2009 [arXiv]Externer Link
  • I. Pavlyukevich
    Lévy flights, non-local search and simulated annealing
    Journal of Computational Physics 226 (2), 1830-1844, 2007 [arXiv]Externer Link
  • I. Pavlyukevich
    Cooling down Lévy flights
    Journal of Physics A: Mathematical and Theoretical 40, 12299-12313, 2007 [arXiv]Externer Link
  • I. Pavlyukevich
    Simulated annealing for Lévy-driven jump-diffusions
    Stochastic Processes and their Applications 118 (6), 1071-1105, 2008
  • P. Imkeller and I. Pavlyukevich
    Lévy flights: transitions and meta-stability
    Journal of Physics A: Mathematical and General 39, L237-L246, 2006
  • P. Imkeller and I. Pavlyukevich
    Metastable behaviour of small noise Lévy-driven diffusions
    ESAIM: Probability and Statistics 12, 412-437, 2008 [arXiv]Externer Link
  • I. Pavlyukevich
    Ruin probabilities of small noise jump-diffusions with heavy tails
    Applied Stochastic Models in Business and Industry 24 (1), 65-82, 2008
  • P. Imkeller and I. Pavlyukevich
    First exit times of SDEs driven by stable Lévy processes
    Stochastic Processes and their Applications 116 (4), 611-642, 2006 [arXiv]Externer Link
  • S. Herrmann, P. Imkeller and I. Pavlyukevich
    Two mathematical approaches to stochastic resonance
    in J.-D. Deuschel and A. Greven (eds.), Interacting Stochastic Systems, Springer, 2004
  • P. Imkeller and I. Pavlyukevich
    Stochastic resonance: a comparative study of two-state models
    in R. Dalang, M. Dozzi and F. Russo (eds.), Seminar on stochastic analysis, random fields and applications IV, Progress in Probability 58, Birkhäuser Verlag, 2004
  • P. Imkeller and I. Pavlyukevich
    The reduction of potential diffusions to finite state Markov chains and stochastic resonance
    in S. N. Namachchivaya and Y. K. Lin (eds.), IUTAM symposium on nonlinear stochastic dynamics. Proceedings of the IUTAM symposium, Monticello, IL, USA, Augsut 26-30, 2002, Solid Mechanics and Its Applications. 110. Dordrecht: Kluwer Academic Publishers, 2003
  • S. Herrmann, P. Imkeller and I. Pavlyukevich
    Stochastic resonance: non-robust and robust tuning notions
    in K. Haman, B. Jakubiak and J. Zabczyk (eds.), Probabilistic Problems in Atmospheric and Water Sciences. Proceedings of the Workshop held at the Bedlewo Mathematical Conference Center, December 16-18, 2002, Banach Center Publ., 2003
  • P. Imkeller and I. Pavlyukevich
    Model reduction and stochastic resonance
    Stochastics and Dynamics 2 (4), 463-506, 2002
  • P. Imkeller and I. Pavlyukevich
    Stochastic resonance in two-state Markov chains
    Archiv der Mathematik 77 (1), 107-115, 2001 [arXiv]Externer Link
  • I. Pavlyukevich
    On the calculation of probability characteristics of some optimal stopping times
    Russian Mathematical Surveys 51 (1), 228-229, 1997
Abschlussarbeiten
  • Dissertation: Stochastic Resonance
    2002. Betreuer: Peter Imkeller
  • Diplomarbeit: Look-back Perpetual Option of American Type
    1986. Betreuer: Albert Shiryaev
Arbeitsgebiete
  • Stochastische Prozesse und deren Anwendungen
  • Dynamische Systeme mit kleinem Rauschen
  • Große Abweichungen
  • Stochastische Resonanz
  • Lévyprozesse
  • Schwere Ränder
  • Stabile Prozesse und Lévyflüge
  • Metastabilität
  • First Exit Times
  • Nicht-lokale Suche und Simulated Annealing
  • Einfache Klimamodelle
  • SPDEs mit Lévy-Rauschen
  • Statistik von Sprung-Diffusionen

Lehre

WS 2022/23

  • Stochastic Processes
  • Oberseminar Stochastik