Large deviations of conservative stochastic partial differential equations

TL;DR

This paper proves a large deviation principle for conservative stochastic partial differential equations, linking their solutions to stochastic differential equations with interaction, using weak convergence and contraction principles.

Contribution

It introduces a large deviation framework for conservative SPDEs, connecting them to stochastic differential equations with interaction, advancing theoretical understanding.

Findings

Established a large deviation principle for conservative SPDEs

Connected solutions of SPDEs to stochastic differential equations with interaction

Utilized weak convergence and contraction principles in the proof

Abstract

In this paper, we establish a large deviation principle for the conservative stochastic partial differential equations, whose solutions are related to stochastic differential equations with interaction. The weak convergence method and the contraction principle in the theory of large deviations play an important role.