Amplitude equations for SPDEs with quadratic nonlinearities forced by additive and multiplicative noise

2021/12/12 by Shiduo Qu, Qu, Shiduo, Wenlei Li +3
Economics, Econometrics and Finance · Engineering · #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2112.06229

openalex publication_date 2021/12/12 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

This article deals with stochastic partial differential equations with quadratic nonlinearities perturbed by small additive and multiplicative noise. We present the approximate solution of the original equation via the amplitude equation and give the rigorous error analysis. For illustration, we apply our main theorems to stochastic Burger's equation.

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