The Kramers problem for SDEs driven by small, accelerated Lévy noise with exponentially light jumps

2019/04/03 by André de Oliveira Gomes, Gomes, André de Oliveira, Michael A. Högele +1
Economics, Econometrics and Finance · Mathematics · #60E07 #60F10 #60H10 #60J05 #60J75 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1904.02125

openalex publication_date 2019/04/03 · openalex created_date 2022/07/24 · openalex updated_date 2026/07/28

Abstract

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 ε-small and (1/ε)-accelerated Lévy 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 ε → 0 which is also known as the Kramers problem in the literature.

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