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arXiv · 1908.03481

Large deviations for stochastic nonlinear systems of slow-fast diffusions with non-Gaussian L\'evy noises

Shenglan Yuan·René Schilling·Jinqiao Duan
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Abstract

We establish the large deviation principle for the slow variables in slow-fast dynamical system driven by both Brownian noises and L\'evy 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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Shenglan Yuan, René Schilling, Jinqiao Duan. 2019-08-09. Large deviations for stochastic nonlinear systems of slow-fast diffusions with non-Gaussian L\'evy noises. https://doi.org/10.1016/j.ijnonlinmec.2022.104304

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