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Sbornik: Mathematics, 2011, Volume 202, Issue 11, Pages 1565–1592
DOI: https://doi.org/10.1070/SM2011v202n11ABEH004199 (Mi sm7686) 		 
This article is cited in 20 scientific papers (total in 20 papers)

Regularized and generalized solutions of infinite-dimensional stochastic problems

M. A. Alshanskiy, I. V. Mel'nikova

Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
English version PDF (454 kB) Citations (20)
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DOI: https://doi.org/10.1070/SM2011v202n11ABEH004199
Abstract: The paper is concerned with solutions of Cauchy's problem for stochastic differential-operator equations in separable Hilbert spaces. Special emphasis is placed on the case when the operator coefficient of the equation is not a generator of a $C_0$-class semigroup, but rather generates some regularized semigroup. Regularized solutions of equations in the Itô form with a Wiener process as an inhomogeneity and generalized solutions of equations with white noise are constructed in various spaces of abstract distributions.
Bibliography: 23 titles.
Keywords: regularized semigroup of operators, abstract distribution, generalized solution, Wiener process, white noise.
Received: 29.01.2010 and 02.02.2011
Russian version:
Matematicheskii Sbornik, 2011, Volume 202, Number 11, Pages 3–30
DOI: https://doi.org/10.4213/sm7686
Bibliographic databases:
Document Type: Article
UDC: 517.983+517.982.4+519.21
MSC: Primary 60H10, 34F05; Secondary 47D60, 47D62
Language: English
Original paper language: Russian
Citation: M. A. Alshanskiy, I. V. Mel'nikova, “Regularized and generalized solutions of infinite-dimensional stochastic problems”, Mat. Sb., 202:11 (2011), 3–30; Sb. Math., 202:11 (2011), 1565–1592
Citation in format AMSBIB
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    • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:60
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