Existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay
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.
neutral stochastic functional differential equations
scientific article; zbMATH DE number 5648684
scientific article