Existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay (Q1045809)

The authors prove an existence and uniqueness result for a neutral stochastic delay differential equation with unbounded delay driven by Brownian motion with initial condition in the state space of bounded continuous functions on \((-\infty,0]\) taking values in \({\mathbb R}^d\). Their basic assumption is a local Lipschitz and a linear growth condition on the coefficients with respect to the supremum norm on the state space. The existence proof is based on the usual successive approximation procedure.