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Equations with Random Gaussian Operators with Unbounded Mean Value

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Ukrainian Mathematical Journal Aims and scope

Abstract

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.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    M. A. Vlasenko

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  1. M. A. Vlasenko
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Vlasenko, M.A. Equations with Random Gaussian Operators with Unbounded Mean Value. Ukrainian Mathematical Journal 54, 207–217 (2002). https://doi.org/10.1023/A:1020130411493

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  • DOI: https://doi.org/10.1023/A:1020130411493

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