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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 396, Pages 111–143 (Mi znsl4655)  
This article is cited in 9 scientific papers (total in 9 papers)

A probabilistic approximation of the Cauchy problem solution of some evolution equations

I. A. Ibragimovab, N. V. Smorodinac, M. M. Faddeevc

a St. Petersburg State University, Faculty of Mathematics and Mechanics, St. Petersburg, Russia
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
c St. Petersburg State University, Faculty of Physics, St. Petersburg, Russia
Full-text PDF (718 kB) Citations (9)
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Abstract: In our paper we construct an analogy of a probabilistic representation of the Cauchy problem solution of the equation $\frac{\partial u}{\partial t}+\frac{\sigma^2}2\frac{\partial^2u}{\partial x^2}+f(x)u=0$, where $\sigma$ is a complex number.
Key words and phrases: random processes, evolution equations, limit theorems, Feynman–Kac formula.
Received: 11.10.2011
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 188, Issue 6, Pages 700–716
DOI: https://doi.org/10.1007/s10958-013-1161-8
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
Citation: I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “A probabilistic approximation of the Cauchy problem solution of some evolution equations”, Probability and statistics. Part 17, Zap. Nauchn. Sem. POMI, 396, POMI, St. Petersburg, 2011, 111–143; J. Math. Sci. (N. Y.), 188:6 (2013), 700–716
Citation in format AMSBIB
\Bibitem{IbrSmoFad11}
\by I.~A.~Ibragimov, N.~V.~Smorodina, M.~M.~Faddeev
\paper A probabilistic approximation of the Cauchy problem solution of some evolution equations
\inbook Probability and statistics. Part~17
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 396
\pages 111--143
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4655}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2870136}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 188
\issue 6
\pages 700--716
\crossref{https://doi.org/10.1007/s10958-013-1161-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84880603166}
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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