Equations with Random Gaussian Operators with Unbounded Mean Value
We consider an equation in a Hilbert space with a random operator represented as a sum of a deterministic, closed, densely defined operator and a Gaussian strong random operator. We represent a solution of an equation with random right-hand side in terms of stochastic derivatives of solutions of an equation with deterministic right-hand side. We consider applications of this representation to the anticipating Cauchy problem for a stochastic partial differential equation.
English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 2, pp 207-217.
Citation Example: Vlasenko M. A. Equations with Random Gaussian Operators with Unbounded Mean Value // Ukr. Mat. Zh. - 2002. - 54, № 2. - pp. 170-177.