Averaging principle of stochastic Burgers equation driven by Lévy processes

2021/12/11 by Hongge Yue, Yue, Hongge, Yong Xu +5 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Mathematical Biology Tumor Growth #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2112.05906

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 Lévy 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.

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