Large deviation principle for one-dimensional SDEs with discontinuous coefficients

TL;DR

This paper proves a large deviation principle for one-dimensional stochastic differential equations with discontinuous coefficients, extending classical results to cases with weaker assumptions on the nature of discontinuities.

Contribution

It introduces a large deviation principle for SDEs with discontinuous coefficients under weaker conditions than previously required.

Findings

Established large deviation principle for SDEs with discontinuous coefficients

Extended classical Wentzel--Freidlin theorem to weaker discontinuity assumptions

Provided a framework for analyzing rare events in such SDEs

Abstract

We establish the large deviation principle for solutions of one-dimensional SDEs with discontinuous coefficients. The main statement is formulated in a form similar to the classical Wentzel--Freidlin theorem, but under the considerably weaker assumption that the coefficients have no discontinuities of the second kind.