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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) Russian version article
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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
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”, Sb. Math., 202:11 (2011), 1565–1592
Citation in format AMSBIB
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\vol 202
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\pages 1565--1592
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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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    Abstract page:724
    Russian version PDF:196
    English version PDF:19
    References:68
    First page:24
     
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