Solution of Certain Stochastic Differential Equations: Pseudo S-asymptotically Omega Periodic Solution with Measures

Abstract

This research paper discusses a mathematical concept known as the ω-periodic process, and displays a new type of function called the doubly measure pseudo S-asymptotically ω-periodic function. It explores the properties of these functions and uses them to examine the solution of a stochastic differential equation guided by Brownian motion. The main target of the current work is to establish the existence and uniqueness of this solution.