Asymptotic first exit times of the chafee-infante equation with small heavy-tailed levy noise

This article studies the behavior of stochastic reaction-diffusion equations driven by additive regularly varying pure jump Levy 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.

Metadaten
Author details:	Arnaud Debussche, Michael Högele GND, Peter Imkeller
ISSN:	1083-589X
Title of parent work (English):	Electronic communications in probability
Publisher:	Univ. of Washington, Mathematics Dep.
Place of publishing:	Seattle
Publication type:	Article
Language:	English
Year of first publication:	2011
Publication year:	2011
Release date:	2017/03/26
Tag:	first exit times; regularly varying Levy process; small noise asymptotics; stochastic reaction diffusion equation with heavy-tailed Levy noise
Volume:	16
Issue:	3-4
Number of pages:	13
First page:	213
Last Page:	225
Funding institution:	IRTG SMCP Berlin-Zurich; Berlin Mathematical School
Organizational units:	Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer review:	Referiert