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

摘要

In this work,neutral stochastic functional differential equations with infinite delay(NSFDEw ID)have been addressed.By using the Euler-Maruyama scheme and a localization argument,the existence and uniqueness of solutions to NSFDEw ID at the state space Cr under the local weak monotone condition,the weak coercivity condition and the global condition on the neutral term have been investigated.In addition,the L2 and exponential estimates of NSFDEw ID have been studied.