Translator Disclaimer
2011 Asymptotic first exit times of the Chafee-Infante equation with small heavy-tailed Lévy noise
Arnaud Debussche, Michael Hoegele, Peter Imkeller
Author Affiliations +
Electron. Commun. Probab. 16: 213-225 (2011). DOI: 10.1214/ECP.v16-1622

Abstract

This article studies the behavior of stochastic reaction-diffusion equations driven by additive regularly varying pure jump L'evy noise in the limit of small noise intensity. It is shown that the law of the suitably renormalized first exit times from the domain of attraction of a stable state converges to an exponential law of parameter 1 in a strong sense of Laplace transforms, including exponential moments. As a consequence, the expected exit times increase polynomially in the inverse intensity, in contrast to Gaussian perturbations, where this growth is known to be of exponential rate.

Citation

Download Citation

Arnaud Debussche. Michael Hoegele. Peter Imkeller. "Asymptotic first exit times of the Chafee-Infante equation with small heavy-tailed Lévy noise." Electron. Commun. Probab. 16 213 - 225, 2011. https://doi.org/10.1214/ECP.v16-1622

Information

Accepted: 18 April 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1233.60037
MathSciNet: MR2788893
Digital Object Identifier: 10.1214/ECP.v16-1622

Subjects:
Primary: 60H15
Secondary: 35R69, 60G51, 60J75, 92F99

JOURNAL ARTICLE
13 PAGES


SHARE
Back to Top