Uniform large deviation principles for SDEs under locally weak monotonicity conditions

TL;DR

This paper establishes uniform large deviation principles for stochastic differential equations with locally weak monotonicity and Lyapunov conditions, broadening applicability to systems with polynomial growth and degenerate noises.

Contribution

It introduces a criterion for ULDP under weaker conditions, extending previous results to more general stochastic systems including Hamiltonian systems.

Findings

Provides a new criterion for ULDP under weak monotonicity

Applicable to systems with polynomial growth and degenerate noise

Extends previous large deviation results to broader classes of SDEs

Abstract

In this paper, we provide a criterion on uniform large deviation principles (ULDP) for stochastic differential equations under locally weak monotone conditions and Lyapunov conditions, which can be applied to stochastic systems with coefficients of polynomial growth and possible degenerate driving noises, including the stochastic Hamiltonian systems. The weak convergence method plays an important role in obtaining the ULDP. This result extends the scope of applications of the main theorem in \cite{WYZZ}.