Problem of large deviations for Markov random evolutions with independent increments in the scheme of asymptotically small diffusion

Abstract

The problem of large deviations for random evolutions with independent increments is solved in the scheme of asymptotically small diffusion by passing to the limit in the nonlinear (exponential) generator of semigroups by using the solution of the problem of singular perturbation for a reducibly invertible operator.