Well-Posedness of the Cauchy Problem for Stochastic Evolution Functional Equations

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We prove the existence, uniqueness, and continuous dependence on the initial data of the solutions of the Cauchy problem for stochastic evolution functional equations with random coefficients in Hilbert spaces. We propose a method for constructing an approximating sequence for the solution of the Cauchy problem and obtain an estimate for the rate of convergence to the exact solution.