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 (defined in Section 3). An example is given to
illustrate the theory.

Keywords

• Existence
• Stability
• Random impulsive
• Stochastic differential system
• Banach fixed point theorem

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