TY  - JOUR
A1  - Debussche, Arnaud
A1  - Högele, Michael
A1  - Imkeller, Peter
T1  - Asymptotic first exit times of the chafee-infante equation with small heavy-tailed levy noise
JF  - Electronic communications in probability
N2  - 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.
KW  - stochastic reaction diffusion equation with heavy-tailed Levy noise
KW  - first exit times
KW  - regularly varying Levy process
KW  - small noise asymptotics
Y1  - 2011
SN  - 1083-589X
VL  - 16
IS  - 3-4
SP  - 213
EP  - 225
PB  - Univ. of Washington, Mathematics Dep.
CY  - Seattle
ER  -