Stochastic differential equations with non-lipschitz coefficients: I. Pathwise uniqueness and large deviation

TL;DR

This paper investigates stochastic differential equations with non-Lipschitz coefficients, establishing pathwise uniqueness of solutions and deriving a large deviation principle of Freidlin-Wentzell type.

Contribution

It provides the first rigorous proof of strong solution uniqueness and large deviation principles for this class of equations with non-Lipschitz coefficients.

Findings

Unique strong solutions are proven to exist.

A large deviation principle of Freidlin-Wentzell type is established.

The results extend the theory to equations with non-Lipschitz coefficients.

Abstract

We study a class of stochastic differential equations with non-Lipschitzian coefficients.A unique strong solution is obtained and a large deviation principle of Freidln-Wentzell type has been established.