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Publications


Book

S. Herrmann, P. Imkeller, I. Pavlyukevich and D. Peithmann
Stochastic resonance: A mathematical approach in the small noise limit
volume 194 of the AMS Mathematical Surveys and Monographs, 2014

Papers (in order of being written)

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
to appear in Nonlinearity, http://arxiv.org/abs/1510.08919

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, http://arxiv.org/abs/1501.03264

A. Chechkin and I. Pavlyukevich
Marcus versus Stratonovich for systems with jump noise
Journal of Physics A: Mathematical and Theoretical, 47, 342001, 2014, http://arxiv.org/abs/1406.0112

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, http://arxiv.org/abs/1405.5433

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, http://arxiv.org/abs/1311.1342

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), 163-190, 2014; http://arxiv.org/abs/1303.5031

R. Hintze and I. Pavlyukevich
Small noise asymptotics of a Lévy flights driven displacement process
Procedia IUTAM, 6, 204-210, 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), 265-281, 2014, http://arxiv.org/abs/1205.6116

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--519, 2011, http://arxiv.org/abs/1205.6115

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 (link)

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), 83-110, 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 (link), arXiv.org/abs/0804.2276

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 (link), (pdf), arXiv:0711.0982

I. Pavlyukevich
Lévy flights, non-local search and simulated annealing
Journal of Computational Physics 226 (2), 1830-1844, 2007 (link), arXiv:cond-mat/0701653

I. Pavlyukevich
Cooling down Lévy flights
Journal of Physics A: Mathematical and Theoretical 40, 12299-12313, 2007 (link), arXiv:cond-mat/0701651

I. Pavlyukevich
Simulated annealing for Lévy-driven jump-diffusions
Stochastic Processes and their Applications 118 (6), 1071-1105, 2008 (link).

P. Imkeller and I. Pavlyukevich
Lévy flights: transitions and meta-stability
Journal of Physics A: Mathematical and General 39, L237-L246, 2006 (link), (pdf).

P. Imkeller and I. Pavlyukevich
Metastable behaviour of small noise Lévy-driven diffusions
ESAIM: Probability and Statistics 12, 412-437, 2008 (link), (pdf), arXiv:math/0601771

I. Pavlyukevich
Ruin probabilities of small noise jump-diffusions with heavy tails
Applied Stochastic Models in Business and Industry 24 (1), 65-82, 2008 (link).

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 (link), arXiv:math/0409246

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 (pdf)

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 (pdf)

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 (pdf)

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 (pdf)

P. Imkeller and I. Pavlyukevich
Model reduction and stochastic resonance
Stochastics and Dynamics 2 (4), 463-506, 2002 (link), (pdf)

P. Imkeller and I. Pavlyukevich
Stochastic resonance in two-state Markov chains
Archiv der Mathematik 77 (1), 107-115, 2001 (link), arXiv:math/0302359

I. Pavlyukevich
On the calculation of probability characteristics of some optimal stopping times
Russian Mathematical Surveys 51 (1), 228-229, 1997


PhD Thesis

Stochastic resonance. 2002. PDF (1.1 MB), DjVu (952 KB)