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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 431, Pages 9–36 (Mi znsl6092)  
This article is cited in 3 scientific papers (total in 3 papers)

A stochastic model for the Lotka–Volterra system with cross-diffusion

Ya. I. Belopolskaya

St. Petersburg State University of Architecture and Civil Engineering, St. Petersburg, Russia
Full-text PDF (286 kB) Citations (3)
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Abstract: We propose two approaches that allow to construct a probabilistic representation of a generalized solution of the Cauchy problem for a system of quasilinear parabolic equations. The system under consideration presents a population dynamics model for a prey-predator population. We construct two types of stochastic problem associated with this parabolic system that give the way to derive the required probabilistic representation.
Key words and phrases: stochastic differential equations, stochastic flows, systems of quasilinear parabolic equations, genaralized solutions of the Cauchy problem.
Received: 11.11.2014
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 214, Issue 4, Pages 425–442
DOI: https://doi.org/10.1007/s10958-016-2787-0
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
Citation: Ya. I. Belopolskaya, “A stochastic model for the Lotka–Volterra system with cross-diffusion”, Probability and statistics. Part 21, Zap. Nauchn. Sem. POMI, 431, POMI, St. Petersburg, 2014, 9–36; J. Math. Sci. (N. Y.), 214:4 (2016), 425–442
Citation in format AMSBIB
\Bibitem{Bel14}
\by Ya.~I.~Belopolskaya
\paper A stochastic model for the Lotka--Volterra system with cross-diffusion
\inbook Probability and statistics. Part~21
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 431
\pages 9--36
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6092}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3488634}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 214
\issue 4
\pages 425--442
\crossref{https://doi.org/10.1007/s10958-016-2787-0}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84961123259}
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  • https://www.mathnet.ru/eng/znsl/v431/p9
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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