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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, Number 5, Pages 12–27 (Mi ivm8891)  
This article is cited in 1 scientific paper (total in 1 paper)

Connection between weak and generalized solutions of infinite-dimensional stochastic problems

I. V. Mel'nikovaa, O. S. Starkovab

a Chair of Mathematical Analysis and Function Theory, Ural Federal University, 51 Lenin Ave., Ekaterinburg, 620083 Russia
b Problem-Scientific Laboratory of Applied Analysis, Ural Federal University, 51 Lenin Ave., Ekaterinburg, 620083 Russia
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Abstract: We investigate the stochastic Cauchy problem for the first order equation with singular white noise and generators of regularized (integrated, convoluted) semigroups in Hilbert spaces and abstract distribution spaces. Weak solutions for the problem in the Ito form and generalized solutions for the differential problem in abstract distribution spaces are constructed in dependence on properties of the generator. Connections between these solutions are shown.
Keywords: distribution, semigroup of operators, white noise, Wiener process, generalized solution, weak solution, regularized solution.
Received: 16.11.2012
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2014, Volume 58, Issue 5, Pages 8–20
DOI: https://doi.org/10.3103/S1066369X14050028
Bibliographic databases:
Document Type: Article
UDC: 517.983+517.982+519.21
Language: Russian
Citation: I. V. Mel'nikova, O. S. Starkova, “Connection between weak and generalized solutions of infinite-dimensional stochastic problems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 5, 12–27; Russian Math. (Iz. VUZ), 58:5 (2014), 8–20
Citation in format AMSBIB
\Bibitem{MelSta14}
\by I.~V.~Mel'nikova, O.~S.~Starkova
\paper Connection between weak and generalized solutions of infinite-dimensional stochastic problems
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2014
\issue 5
\pages 12--27
\mathnet{http://mi.mathnet.ru/ivm8891}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2014
\vol 58
\issue 5
\pages 8--20
\crossref{https://doi.org/10.3103/S1066369X14050028}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899831776}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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