Asymptotic methods for stochastic dynamical systems with small non-Gaussian Lévy noise

Details Asymptotic methods for stochastic dynamical systems with small non-Gaussian Lévy noise Asymptotic methods for stochastic dynamical systems with small non-Gaussian Lévy noise

2012-01-04

arxiv.org/abs/1201.0829v1

Mathematics

Probability

19 pages,1 figure

Scientific paper

The escape probability is a deterministic tool that quantifies some aspects of stochastic dynamics. The goal of the present work is to analytically examine escape probabilities for dynamical systems driven by symmetric $\alpha$-stable L\'evy motions. Since escape probabilities are solutions of a type of integro-differential equations (i.e., differential equations with nonlocal interactions), asymptotic methods are offered to solve these equations to obtain escape probabilities when noise is sufficiently small. Two examples are presented to illustrate the asymptotic methods, and asymptotic escape probability is compared with numerical simulations.

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