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Existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay. (English) Zbl 1195.34123
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 $\left(-\infty ,0\right]$ taking values in ${ℝ}^{d}$. 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.
##### MSC:
 34K50 Stochastic functional-differential equations 34K05 General theory of functional-differential equations 34K40 Neutral functional-differential equations 47N20 Applications of operator theory to differential and integral equations
##### References:
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