On the Stochastic Evolution Equation Driven by Brownian Motion in a Separable Space

被引：0
作者：
Mohsen Miraoui
Sonia Missaoui
机构：
[1] IPEIK,
[2] Kairouan University,undefined
[3] FSS,undefined
[4] Sfax University,undefined
来源：
Complex Analysis and Operator Theory | 2023年 / 17卷
关键词：
Pseudo almost periodic solution; Stochastic processes; Stochastic evolution equations; Measure theory; Fixed point theorem; Brownian motion; 60H15; 60G51; 34C27; 35R60;
D O I：
暂无
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学科分类号：
摘要：
This article discusses issues surrounding the concept of a double measure Stepanov-type pseudo-almost periodic (‘pap’) mean-square process with a double measures. Moreover, using stochastic analysis techniques and Banach’s fixed point Theorem, we investigate the uniqueness and existence of the ‘pap’ solution to partial stochastic neutral differential equations with double measure mean-square ’pap’ coefficients of the Stepanov type driven by the Brownian motion in a separable Hilbert space K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {K}}$$\end{document}. Therefore, we study its global exponential stability. The concluding segment of our work is exemplified by a practical illustration, affirming the reliability and applicability of our findings.
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