Existence Uniqueness and Stability of Nonlocal Neutral Stochastic Differential Equations with Random Impulses and Poisson Jumps

Abstract

This manuscript aims to investigate the existence, uniqueness, and stability of non-local random impulsive neutral stochastic differential time delay equations (NRINSDEs) with Poisson jumps. First, we prove the existence of mild solutions to this equation using the Banach fixed point theorem. Next, we prove the stability via continuous dependence initial value. Our study extends the work of Wang and Wu [15] where the time delay is addressed by the prescribed phase space B (dened in Section 3). An example is given to illustrate the theory.