On the small time asymptotics of quasilinear parabolic stochastic partial differential equations

TL;DR

This paper establishes small time large deviation principles for quasilinear parabolic stochastic PDEs with multiplicative noise, expanding understanding of their probabilistic behavior in short time scales.

Contribution

It introduces a novel approach to analyze non-monotone quasilinear stochastic PDEs, providing new theoretical insights into their small time asymptotics.

Findings

Proved small time large deviation principles for a class of stochastic PDEs.

Extended large deviation theory to non-monotone quasilinear equations.

Enhanced understanding of short-term probabilistic behavior of complex stochastic systems.

Abstract

In this paper, we establish a small time large deviation principles for the quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone.