Mean Exit Time and Escape Probability for Dynamical Systems Driven by Lévy Noises

2014/01/01 by T. Gao, Ting Gao, Jinqiao Duan +5 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Physics and Astronomy · #Probabilistic and Robust Engineering Design #Stochastic processes and financial applications #stochastic dynamics and bifurcation

paper · doi:10.1137/120897262

openalex publication_date 2014/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

The mean first exit time and escape probability are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian α-stable type Lévy motions. An efficient and accurate numerical scheme is developed and validated for computing the mean exit time and escape probability from the governing differential-integral equation. An asymptotic solution for the mean exit time is given when the pure jump measure in the Lévy motion is small. From both the analytical and numerical results, it is observed that the mean exit time depends strongly on the domain size and the value of α in the α-stable Lévy jump measure. The mean exit time and escape probability could become discontinuous at the boundary of the domain, when the value of α is in (0,1).

Citations

• Random dynamical systems
• Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints

Cited by

• Mean exit time for stochastic dynamical systems driven by tempered stable Lévy fluctuations

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