Large deviations for random evolutions with independent increments in the scheme of L\'evy approximation

TL;DR

This paper analyzes the large deviations behavior of random evolutions with independent increments within the framework of Lévy approximation, using exponential generators to characterize the deviations.

Contribution

It provides a new asymptotic analysis of large deviations for random evolutions in the Lévy approximation scheme, focusing on exponential generators.

Findings

Large deviations are characterized by exponential generators.

The analysis applies to random evolutions with independent increments.

Results contribute to the understanding of Lévy process approximations.

Abstract

In the work asymptotic analysis of the problem of large deviations for random evolutions with independent increments in the circuit of L\'{e}vy approximation is carried out. Large deviations for random evolutions in the circuit of Levy approximation are determined by exponential generator for jumping process with independent increments.