Invariant measures for stochastic Burgers equation in unbounded domains with space-time white noise

2024/01/27 by Zhenxin Liu, Liu, Zhenxin, Zhiyuan Shi +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #35Q35 #35R60 #60H15 #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical methods in inverse problems #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2401.15349

openalex publication_date 2024/01/27 · openalex created_date 2024/02/01 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the stochastic damped Burgers equation with multiplicative space-time white noise defined on the entire real line. We prove the existence and uniqueness of a mild solution of the stochastic damped Burgers equation in the weighted space and establish that the solution is bounded in probability. Furthermore, by using the Krylov-Bogolioubov theorem, we obtain the existence of invariant measures.

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