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arXiv · 2207.07081

Large Deviations for Lévy Diffusions in small regime

Pedro Catuogno·André de Oliveira Gomes
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Abstract

This article concerns the large deviations regime and the consequent solution of the Kramers problem for a two-time scale stochastic system driven by a common jump noise signal perturbed in small intensity $\varepsilon>0$ and with accelerated jumps by intensity $\frac{1}{\varepsilon}$. We establish Freidlin-Wentzell estimates for the slow process of the multiscale system in the small noise limit $\varepsilon \rightarrow 0$ using the weak convergence approach to large deviations theory. The core of our proof is the reduction of the large deviations principle to the establishment of a stochastic averaging principle for auxiliary controlled processes. As consequence we solve the first exit time/ exit locus problem from a bounded domain containing the stable state of the averaged dynamics for the family of the slow processes in the small noise limit.

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Pedro Catuogno, André de Oliveira Gomes. 2022-07-14. Large Deviations for Lévy Diffusions in small regime. https://arxiv.org/abs/2207.07081

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