Prof. Dr. Ilya Pavlyukevich

Ilya Pavlyukevich, Univ.-Prof. Dr.
Raum 3526
Ernst-Abbe-Platz 1-2
07743 Jena Google Maps – LageplanExterner Link

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