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

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.