Averaging principle of stochastic Burgers equation driven by L\'{e}vy processes

TL;DR

This paper establishes an averaging principle for a stochastic Burgers equation driven by Lévy processes, demonstrating that the slow component converges to a limit characterized by averaged coefficients, supported by numerical simulations.

Contribution

It extends the averaging principle to stochastic Burgers equations with Lévy noise, providing theoretical convergence results and numerical illustrations.

Findings

Strong convergence of the slow component to the averaged limit

Characterization of the limit by the solution of an averaged stochastic Burgers equation

Numerical simulations confirming theoretical results

Abstract

We are concerned about the averaging principle for the stochastic Burgers equation with slow-fast time scale. This slow-fast system is driven by L\'{e}vy processes. Under some appropriate conditions, we show that the slow component of this system strongly converges to a limit, which is characterized by the solution of stochastic Burgers equation whose coefficients are averaged with respect to the stationary measure of the fast-varying jump-diffusion. To illustrate our theoretical result, we provide some numerical simulations.