@inproceedings{efd8235969814418ab8f82f5b78a3f9f,
title = "Escape Probability for Stochastic Dynamical Systems with Jumps",
abstract = "The escape probability is a deterministic concept that quantifies some aspects of stochastic dynamics. This issue has been investigated previously for dynamical systems driven by Gaussian Brownian motions. The present work considers escape probabilities for dynamical systems driven by non-Gaussian L{\'e}vy motions, especially symmetric α-stable L{\'e}vy motions. The escape probabilities are characterized as solutions of the Balayage-Dirichlet problems of certain partial differential-integral equations. Differences between escape probabilities for dynamical systems driven by Gaussian and non-Gaussian noises are highlighted. In certain special cases, analytic results for escape probabilities are given.",
keywords = "Balayage-Dirichlet problem, Discontinuous stochastic dynamical systems, Escape probability, L{\'e}vy processes, Non-Gaussian noise, Nonlocal differential equation",
author = "Huijie Qiao and Xingye Kan and Jinqiao Duan",
note = "Copyright: Copyright 2014 Elsevier B.V., All rights reserved.",
year = "2013",
doi = "10.1007/978-1-4614-5906-4_9",
language = "English (US)",
isbn = "9781461459057",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer New York LLC",
pages = "195--216",
booktitle = "Malliavin Calculus and Stochastic Analysis",
}