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Matematicheskie Trudy, 2019, Volume 22, Number 1, Pages 3–18
DOI: https://doi.org/10.33048/mattrudy.2019.22.101 (Mi mt346) 		 
On stability and comparison theorems for systems of stochastic differential equations

A. S. Asylgareev

Ufa State Aviation Technical University, Ufa, 450000 Russia
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DOI: https://doi.org/10.33048/mattrudy.2019.22.101
Abstract: We prove comparison theorems for stochastic differential equations (briefly, SDE) with respect to a standard multidimensional Wiener process as well as for components of systems of SDE with respect to a multidimensional Wiener process. The obtained results are applied to the study of the stability with probability 1 of the perturbed solutions to the SDE.
Key words: stability with probability 1, stochastic differential equation, comparison theorem, multidimensional Wiener process, Itô integral, Stratonovich integral.
Received: 26.02.2018
Revised: 26.02.2018
Accepted: 10.10.2018
English version:
Siberian Advances in Mathematics, 2019, Volume 29, Issue 3, Pages 153–163
DOI: https://doi.org/10.3103/S1055134419030015
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
Citation: A. S. Asylgareev, “On stability and comparison theorems for systems of stochastic differential equations”, Mat. Tr., 22:1 (2019), 3–18; Siberian Adv. Math., 29:3 (2019), 153–163
Citation in format AMSBIB
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\by A.~S.~Asylgareev
\paper On~stability and comparison theorems for~systems of~stochastic differential equations
\jour Mat. Tr.
\yr 2019
\vol 22
\issue 1
\pages 3--18
\mathnet{http://mi.mathnet.ru/mt346}
\crossref{https://doi.org/10.33048/mattrudy.2019.22.101}
\transl
\jour Siberian Adv. Math.
\yr 2019
\vol 29
\issue 3
\pages 153--163
\crossref{https://doi.org/10.3103/S1055134419030015}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85071488333}
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    		Математические труды Siberian Advances in Mathematics
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