Escape Probability for Stochastic Dynamical Systems with Jumps

Huijie Qiao; Xingye Kan; Jinqiao Duan

doi:10.1007/978-1-4614-5906-4_9

Escape Probability for Stochastic Dynamical Systems with Jumps

Huijie Qiao, Xingye Kan, Jinqiao Duan

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Malliavin Calculus and Stochastic Analysis
Subtitle of host publication	A Festschrift in Honor of David Nualart
Publisher	Springer New York LLC
Pages	195-216
Number of pages	22
ISBN (Print)	9781461459057
DOIs	https://doi.org/10.1007/978-1-4614-5906-4_9
State	Published - 2013

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	34
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

Access

10.1007/978-1-4614-5906-4_9

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Escape Probability for Stochastic Dynamical Systems with Jumps. / Qiao, Huijie; Kan, Xingye; Duan, Jinqiao.

Malliavin Calculus and Stochastic Analysis: A Festschrift in Honor of David Nualart. Springer New York LLC, 2013. p. 195-216 (Springer Proceedings in Mathematics and Statistics; Vol. 34).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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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.",

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