数学
不变测度
遍历性
不变(物理)
李普希茨连续性
有界函数
数学分析
遍历理论
反应扩散系统
极限(数学)
限制设置
数学物理
统计
作者
Zhang Chen,Bixiang Wang
标识
DOI:10.1142/s0219493721400128
摘要
This paper deals with invariant measures of fractional stochastic reaction–diffusion equations on unbounded domains with locally Lipschitz continuous drift and diffusion terms. We first prove the existence and regularity of invariant measures, and then show the tightness of the set of all invariant measures of the equation when the noise intensity varies in a bounded interval. We also prove that every limit of invariant measures of the perturbed systems is an invariant measure of the corresponding limiting system. Under further conditions, we establish the ergodicity and the exponentially mixing property of invariant measures.
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