Large deviations for stochastic nonlinear systems of slow-fast diffusions with non-Gaussian Lévy noises

Abstract

We establish the large deviation principle for the slow variables in slow-fast dynamical system driven by both Brownian noises and Lévy noises. The fast variables evolve at much faster time scale than the slow variables, but they are fully inter-dependent. We study the asymptotics of the logarithmic functionals of the slow variables in the three regimes based on viscosity solutions to the Cauchy problem for a sequence of partial integro-differential equations. We also verify the comparison principle for the related Cauchy problem to show the existence and uniqueness of the limit for viscosity solutions.

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• Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited
• Large Deviations and Importance Sampling for Systems of Slow-Fast Motion
• Large Deviations in Fast-Slow Systems
• Large deviations for multi-scale jump-diffusion processes