Existence, Uniqueness and Stability Analysis for Neutral Stochastic Functional Differential Equations with Jumps and Infinite Delay

This work focuses on a class of neutral stochastic functional differential equations with jumps and infinite delay (NSFDEwJI). First, we prove the existence and uniqueness of solution maps to NSFDEwJI using successive construction methods, and provide the exponential estimation of solution maps. Next, we establish the boundedness in pth moment of solution maps by Lyapunov function. Finally, with the aid of the Razumikhin argument, we obtain the exponential stability in pth moment. Based on this, the almost sure exponential stability is derived under a specific condition.