On a Wiener-Poisson equation with rapidly fluctuating coefficients: application to large deviations

In this paper, we deal with a stochastic differential equation with fast oscillating coefficients and with respect to a Brownian motion and a Poisson random measure. The large deviation principle of solution is established, and the effect of the highly nonlinear and locally periodic coefficients is stated. Moreover, we derive an explicit expression for the action functional when the viscosity parameter ε is of order 1 while the homogenization parameter δε tends to zero.