Abstract
The main aim of this article is to show that the solution of a stochastic variational inequality problem obtained from a procedure based on extragradient-like scheme converges in quadratic mean to a unique random fixed point in Hilbert space. Furthermore, the result is applied to optimal control problem defined for a stochastic differential equation with a unit point delay in the state variable. The results generalize, extend, and unify many established results in the literature on deterministic variational inequality problems.
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