Abstract
The first-order abstract Cauchy problem with additive white noise and generator of an R-semigroup in a Hilbert space H is investigated. A generalized solution in spaces of H-valued stochastic distributions is constructed and the main characteristics of the solution are obtained.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 16, Differential and Functional Differential Equations. Part 2, 2006.
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Melnikova, I.V., Filinkov, A. Abstract Cauchy problem in spaces of stochastic distributions. J Math Sci 149, 1567–1579 (2008). https://doi.org/10.1007/s10958-008-0082-4
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DOI: https://doi.org/10.1007/s10958-008-0082-4