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.
Similar content being viewed by others
REFERENCES
A. A. Dorogovtsev, Stochastic Analysis and Random Maps in Hilbert Space, VSP, Utrecht (1994).
K. Kuratowski, Topology, Academic Press, New York (1966-1968).
A. A. Dorogovtsev, “Anticipating equations and filtration problem,” Theor. Stochast. Proc., 3(19), No. 1-2, 154–163 (1997).
W. Rudin, Functional Analysis, McGraw-Hill, New York (1973).
T. Sekiguchi and Y. Shiota, “L-2-theory of noncausal stochastic integrals,” Math. Repts Toyama Univ., 8, 119–195 (1985).
I. Shigekawa, “Derivatives of Wiener functionals and absolute continuity of induced measures,” J. Math. Kyoto Univ., 20, 263–290 (1980).
M. O. Vlasenko, “On anticipating Cauchy problem for stochastic differential equation with partial derivatives,” in: Abstracts of the International Conference “Stochastic Analysis and Its Applications” (June 10-17, 2001, Lviv), Lviv (2001), p. 67.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Issue Date:
DOI: https://doi.org/10.1023/A:1020130411493