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

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.