Large deviations for stochastic nonlinear systems of slow-fast diffusions with non-Gaussian L\'evy noises
Dynamical Systems
2022-11-22 v2
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.
Cite
@article{arxiv.1908.03481,
title = {Large deviations for stochastic nonlinear systems of slow-fast diffusions with non-Gaussian L\'evy noises},
author = {Shenglan Yuan and René Schilling and Jinqiao Duan},
journal= {arXiv preprint arXiv:1908.03481},
year = {2022}
}