TY  - JOUR
A1  - De Oliveira Gomes, André
A1  - Högele, Michael Anton
T1  - The Kramers problem for SDEs driven by small, accelerated Lévy noise with exponentially light jumps
JF  - Stochastics and dynamics
N2  - We establish Freidlin-Wentzell results for a nonlinear ordinary differential equation starting close to the stable state 0, say, subject to a perturbation by a stochastic integral which is driven by an epsilon-small and (1/epsilon)-accelerated Levy process with exponentially light jumps. For this purpose, we derive a large deviations principle for the stochastically perturbed system using the weak convergence approach developed by Budhiraja, Dupuis, Maroulas and collaborators in recent years. In the sequel, we solve the associated asymptotic first escape problem from the bounded neighborhood of 0 in the limit as epsilon -> 0 which is also known as the Kramers problem in the literature.
KW  - Freidlin-Wentzell theory
KW  - large deviations principle
KW  - accelerated small
KW  - noise Levy diffusions
KW  - first passage times
KW  - first exit location
KW  - strongly tempered stable Levy measure
Y1  - 2021
U6  - https://doi.org/10.1142/S0219493721500192
SN  - 0219-4937
SN  - 1793-6799
VL  - 21
IS  - 04
PB  - World Scientific
CY  - Singapore
ER  -