Existence and Stability Results for Second-Order Neutral Stochastic Differential Equations With Random Impulses and Poisson Jumps

Abstract

The objective of this paper is to investigate the existence and stability results of secondorder neutral stochastic functional differential equations (NSFDEs) in Hilbert space. Initially, we establish the existence results of mild solutions of the aforementioned system using the Banach contraction principle. The results are formulated using stochastic analysis techniques. In the later part, we investigate the stability results through the continuous dependence of solutions on initial conditions.

Keywords

• existence
• stability
• banach contraction principle
• second-order neutral stochastic functional differential equations
• random impulse
• stochastic differential system