Well-posedness and Exponential Estimates for the Solutions to Neutral Stochastic Functional Differential Equations with Infinite Delay

TL;DR

This paper investigates the existence, uniqueness, and exponential behavior of solutions to neutral stochastic functional differential equations with infinite delay, under various conditions, providing theoretical insights into their stability and estimates.

Contribution

It establishes the well-posedness and exponential estimates for NSFDEwID solutions under weaker conditions than previously considered.

Findings

Proved existence and uniqueness of solutions under local weak monotone and coercivity conditions.

Derived $\mathcal{L}^{2}$ and exponential estimates for solutions.

Extended analysis to equations with infinite delay in a stochastic setting.

Abstract

In this work, neutral stochastic functional differential equations with infinite delay (NSFDEwID) has been studied. The existence and uniqueness of solutions to NSFDEwID at the state space $ C_{r} $ under the local weak monotone condition, the weak coercivity condition and the global condition on the neutral term have been investigated. In addition, the $ \mathcal{L}^{2} $ and exponential estimates have been studied of NSFDEwID.