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Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 1, Pages 251–267 (Mi timm794)  

This article is cited in 4 scientific papers (total in 4 papers)

The generalized well-posedness of the Cauchy problem for an abstract stochastic equation with multiplicative noise

I. V. Melnikova, M. A. Alshanskiy

Ural Federal University

Abstract: We study the existence, uniqueness, and stability of a solution to the Cauchy problem for a stochastic differential equation with multiplicative noise in the spaces of generalized random variables with values in a Hilbert space.

Keywords: Cauchy problem, semigroup, white noise, generalized solutions.

Full text: PDF file (259 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, 280, suppl. 1, 134–150

Bibliographic databases:

Document Type: Article
UDC: 517.983+517.982.4+519.21
Received: 23.05.2011

Citation: I. V. Melnikova, M. A. Alshanskiy, “The generalized well-posedness of the Cauchy problem for an abstract stochastic equation with multiplicative noise”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 1, 2012, 251–267; Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 134–150

Citation in format AMSBIB
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\paper The generalized well-posedness of the Cauchy problem for an abstract stochastic equation with multiplicative noise
\serial Trudy Inst. Mat. i Mekh. UrO RAN
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\vol 18
\issue 1
\pages 251--267
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2013
\vol 280
\issue , suppl. 1
\pages 134--150
\crossref{https://doi.org/10.1134/S0081543813020119}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84875970155}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. A. Alshanskii, “Integraly Ito i Khitsudy–Skorokhoda v beskonechnomernom sluchae”, Sib. elektron. matem. izv., 11 (2014), 185–199  mathnet
    2. I. V. Melnikova, M. A. Alshanskiy, “White noise calculus in applications to stochastic equations in Hilbert spaces”, Journal of Mathematical Sciences, 218:4 (2016), 395–429  mathnet  crossref
    3. I. V. Melnikova, M. A. Alshanskiy, “Stochastic equations with an unbounded operator coefficient and multiplicative noise”, Siberian Math. J., 58:6 (2017), 1052–1066  mathnet  crossref  crossref  isi  elib
    4. M. A. Alshanskiy, “A model of age-structured population under stochastic perturbation of death and birth rates”, Ural Math. J., 4:1 (2018), 3–13  mathnet  crossref
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