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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 6, Pages 1354–1371
DOI: https://doi.org/10.17377/smzh.2017.58.614 (Mi smj2943) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Stochastic equations with an unbounded operator coefficient and multiplicative noise

I. V. Melnikovaa, M. A. Alshanskiyb

a Ural Federal University, Institute of Natural Sciences and Mathematics, Ekaterinburg, Russia
b Ural Federal University, Institute of Radio Engineering and Information Technologies, Ekaterinburg, Russia
Full-text PDF (360 kB) Citations (3)
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DOI: https://doi.org/10.17377/smzh.2017.58.614
Abstract: Under study is a stochastic operator-differential equation with multiplicative noise in the space of Hilbert-valued generalized random variables. Existence and uniqueness of solutions to the Cauchy problem are proved for the case of an unbounded operator coefficient at the white noise. The equation of population dynamics with a stochastically perturbed multiplication operator is presented as an example.
Keywords: stochastic operator-differential equation, white noise, generalized random variable, S-transform, Wick product, Hitsuda–Skorokhod integral.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-9356.2016.1
02.A03.21.0006
The authors were supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-9356.2016.1) and the URFU Restoring Competitiveness Program (Grant 02.A03.21.0006).
Received: 10.11.2015
Revised: 13.05.2017
English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 6, Pages 1052–1066
DOI: https://doi.org/10.1134/S0037446617060143
Bibliographic databases:
Document Type: Article
UDC: 517.983+517.982.4+519.21
MSC: 35R30
Language: Russian
Citation: I. V. Melnikova, M. A. Alshanskiy, “Stochastic equations with an unbounded operator coefficient and multiplicative noise”, Sibirsk. Mat. Zh., 58:6 (2017), 1354–1371; Siberian Math. J., 58:6 (2017), 1052–1066
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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