Existence, uniqueness, and controllability results for neutral FSDEs in Hilbert spaces. (English) Zbl 1145.93023

Summary: We establish results concerning the global existence, uniqueness, and controllability of mild solutions for a neutral functional stochastic differential equations with variable delay in a real separable Hilbert space. The results are obtained by imposing a so-called Carathéodory condition on the nonlinearities, which is weaker than the classical Lipschitz condition. Examples illustrating the applicability of the general theory are also provided.


93C23 Control/observation systems governed by functional-differential equations
93E03 Stochastic systems in control theory (general)