A Study on Square-Mean <i>S</i>-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument

A Study on Square-Mean <i>S</i>-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument

This work is mainly focused on square-mean <i>S</i>-asymptotically Bloch type periodicity and its applications. The main aim of the paper is to introduce the definition of square-mean <i>S</i>-asymptotically Bloch type periodic processes with values in complex Hilbert spaces...

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Bibliographic Details
Main Authors: Mamadou Moustapha Mbaye, Amadou Diop, Gaston Mandata N’Guérékata
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Mathematics
Subjects:
stochastic processes
stochastic evolution equations
pseudo-S-asymptotically Bloch type periodic functions
Online Access:https://www.mdpi.com/2227-7390/13/9/1495
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Summary:This work is mainly focused on square-mean <i>S</i>-asymptotically Bloch type periodicity and its applications. The main aim of the paper is to introduce the definition of square-mean <i>S</i>-asymptotically Bloch type periodic processes with values in complex Hilbert spaces and systematically analyze some qualitative properties of this type of processes. These properties, combined with the inequality technique, evolution operator theory, fixed-point theory, and stochastic analysis approach, allow us to establish conditions for the existence and uniqueness of square-mean <i>S</i>-asymptotically Bloch type periodicity of bounded mild solutions for a class of stochastic evolution equations with infinite delay and piecewise constant argument. In the end, examples are given to illustrate the feasibility of our results.
ISSN:2227-7390

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