Research Article

Measure pseudo S -asymptotically ω-periodic solution in distribution for some stochastic differential equations with Stepanov pseudo S -asymptotically ω-periodic coefficients

Published in: Quaestiones Mathematicae
Volume 47 , issue 11 , 2024 , pages: 2195–2213

DOI: 10.2989/16073606.2024.2367072

Author(s): Mondher Damak Faculty of Sciences, Sfax University, Tunisia , Ekar Sidi Abdalla Faculty of Sciences, Sfax University, Tunisia

Keywords: 34K14 , 60H10 , 60H20 , Stochastic differential equation , pseudo asymptotically periodic in distribution , Stepanov pseudo asymptotically periodic , doubly measure

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Abstract

In this research paper, a mathematical concept known as the ω-periodic process is discussed, and a new type of processes called the doubly measure pseudo -asymptotically ω-periodic in distribution process is set forward. Additionally, the properties of these processes are identified and invested to tackle the solution of a stochastic differential equation guided by Brownian motion. The basic objective of the current work resides in corroborating the existence and uniqueness of the solution which is doubly measure pseudo -asymptotically ω-periodic in distribution.

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