# Asymptotics for stochastic Burgers equation with jumps

## TL;DR

This paper investigates the long-term behavior and deviation principles of a one-dimensional stochastic Burgers equation influenced by both Brownian motion and Poisson jumps, providing insights into its ergodic properties and rare event probabilities.

## Contribution

It establishes $oldsymbol{ ext{ψ}}$-uniformly exponential ergodicity and derives moderate and large deviation principles for occupation measures of the stochastic Burgers equation with jumps.

## Key findings

- Proves $oldsymbol{ ext{ψ}}$-uniformly exponential ergodicity.
- Derives moderate deviation principle for occupation measures.
- Establishes large deviation principle for occupation measures.

## Abstract

For one-dimensional stochastic Burgers equation driven by Brownian motion and Poisson process, we study the $\psi$-uniformly exponential ergodicity with $\psi(x)=1+\|x\|$, the moderate deviation principle and the large deviation principle for the occupation measures.