Existence and stability of <i>μ</i>-pseudo almost automorphic solutions for stochastic evolution equations

doi:10.1007/s11464-019-0754-z

Front. Math. China

2019, Vol. 14

Issue (2) : 261-280 https://doi.org/10.1007/s11464-019-0754-z

RESEARCH ARTICLE

Existence and stability of μ-pseudo almost automorphic solutions for stochastic evolution equations

Jing CUI(

), Wenping RONG

College of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, China

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Abstract

We introduce a new concept of μ-pseudo almost automorphic processes in p-th mean sense by employing the measure theory, and present some results on the functional space of such processes like completeness and composition theorems. Under some conditions, we establish the existence, uniqueness, and the global exponentially stability of μ-pseudo almost automorphic mild solutions for a class of nonlinear stochastic evolution equations driven by Brownian motion in a separable Hilbert space.

Keywords Stochastic evolution equation μ-pseudo almost automorphic process fixed point theorem

Corresponding Author(s): Jing CUI

Issue Date: 14 May 2019

Cite this article:

Jing CUI,Wenping RONG. Existence and stability of μ-pseudo almost automorphic solutions for stochastic evolution equations[J]. Front. Math. China, 2019, 14(2): 261-280.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0754-z
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I2/261

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