Escape Probability for Stochastic Dynamical Systems with Jumps

Huijie Qiao, Xingye Kan, Jinqiao Duan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Scopus citations


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 Lévy motions, especially symmetric α-stable Lévy 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.

Original languageEnglish (US)
Title of host publicationMalliavin Calculus and Stochastic Analysis
Subtitle of host publicationA Festschrift in Honor of David Nualart
PublisherSpringer New York LLC
Number of pages22
ISBN (Print)9781461459057
StatePublished - 2013

Publication series

NameSpringer Proceedings in Mathematics and Statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Bibliographical note

Funding Information:
We have benefited from our previous collaboration with Ting Gao, Xiaofan Li, and Renming Song. We thank Ming Liao, Renming Song, and Zhen–Qing Chen for helpful discussions. This work was done while Huijie Qiao was visiting the Institute for Pure and Applied Mathematics (IPAM), Los Angeles. This work is partially supported by the NSF of China (No. 11001051 and No. 11028102) and the NSF grant DMS-1025422.


  • Balayage-Dirichlet problem
  • Discontinuous stochastic dynamical systems
  • Escape probability
  • Lévy processes
  • Non-Gaussian noise
  • Nonlocal differential equation


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