数学
不变测度
独特性
随机偏微分方程
数学分析
有界函数
遍历性
布朗运动
分数布朗运动
随机微分方程
偏微分方程
不变(物理)
度量(数据仓库)
遍历理论
数学物理
计算机科学
统计
数据库
作者
Jiaohui Xu,Tomás Caraballo,José Valero
摘要
.This paper is mainly concerned with a kind of fractional stochastic evolution equations driven by Lévy noise in a bounded domain. We first state the well-posedness of the problem via iterative approximations and energy estimates. Then, the existence and uniqueness of weak pullback mean random attractors for the equations are established by defining a mean random dynamical system. Next, we prove the existence of invariant measures when the problem is autonomous by means of the fact that \(H^\gamma (\mathcal{O})\) is compactly embedded in \(L^2(\mathcal{O})\) with \(\gamma \in (0,1)\). Moreover, the uniqueness of this invariant measure is presented, which ensures the ergodicity of the problem. Finally, a large deviation principle result for solutions of stochastic PDEs perturbed by small Lévy noise and Brownian motion is obtained by a variational formula for positive functionals of a Poisson random measure and Brownian motion. Additionally, the results are illustrated by the fractional stochastic Chafee–Infante equations.KeywordsFractional Laplacian operatorLévy noiseBrownian motionweak mean random attractorsinvariant measuresergodicitylarge deviation principleMSC codes35R1135Q3065F0860H1565F10
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