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

Mamadou Moustapha Mbaye, Amadou Diop and Gaston Mandata N’Guérékata ()
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Mamadou Moustapha Mbaye: Laboratoire de Mathématiques Appliquées (LMA), Département de Mathématiques et Informatique, Faculté des Sciences et Technique, Université Cheikh Anta Diop, Fann, Dakar BP 5005, Senegal
Amadou Diop: Classes Préparatoires aux Grandes Écoles (CPGE), Thiès BP A10, Senegal
Gaston Mandata N’Guérékata: NEERLab, Department of Mathematics, Morgan State University, Baltimore, MD 21251, USA

Mathematics, 2025, vol. 13, issue 9, 1-20

Abstract: This work is mainly focused on square-mean S -asymptotically Bloch type periodicity and its applications. The main aim of the paper is to introduce the definition of square-mean S -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 S -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.

Keywords: stochastic processes; stochastic evolution equations; pseudo-S-asymptotically Bloch type periodic functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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