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

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