Large deviation principles for SDEs under locally weak monotonicity conditions

TL;DR

This paper proves a large deviation principle for SDEs with locally weak monotonicity and Lyapunov conditions, extending applicability to models with non-Lipschitz coefficients like biological systems.

Contribution

It introduces a large deviation principle for SDEs under weaker conditions than traditional Lipschitz assumptions, broadening the scope of applicable models.

Findings

Applicable to SDEs with non-Lipschitz coefficients

Includes biological models like stochastic Duffing-van der Pol oscillator

Extends large deviation theory to locally weak monotonicity conditions

Abstract

This paper establishes a Freidlin-Wentzell large deviation principle for stochastic differential equations(SDEs) under locally weak monotonicity conditions and Lyapunov conditions. We illustrate the main result of the paper by showing that it can be applied to SDEs with non-Lipschitzian coefficients, which can not be covered in the existing literature. These include the interesting biological models like stochastic Duffing-van der Pol oscillator model, stochastic SIR model, etc.