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

Autor(es)

Gomes, Andre de Oliveira ^{[1, 2]} ; Hoegele, Michael A. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Matemat, BR-13081970 Campinas, SP - Brazil

^[2] Univ Potsdam, Inst Math, Potsdam - Germany

^[3] Univ Los Andes, Dept Matemat, Bogota - Colombia

• Tipo de documento: Artigo Científico
• Fonte: Stochastics and Dynamics; v. 21, n. 04 JUN 2021.
• Citações Web of Science: 0

Resumo

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. (AU)

• Processo FAPESP: 18/06531-1 - Sistemas Dinâmicos Perturbados por Processos de Lévy
• Beneficiário: André de Oliveira Gomes
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado