Escape Probability for Stochastic Dynamical Systems with Jumps

Huijie Qiao, Xingye Kan, Jinqiao Duan

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

11 Scopus citations

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 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
Pages195-216
Number of pages22
ISBN (Print)9781461459057
DOIs
StatePublished - 2013

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume34
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Keywords

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

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