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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 454, Pages 158–175 (Mi znsl6390)  
This article is cited in 18 scientific papers (total in 19 papers)

On a limit theorem related to probabilistic representation of the Cauchy problem solution for the Schrödinger equation

I. A. Ibragimovab, N. V. Smorodinaab, M. M. Faddeevb

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia
Full-text PDF (229 kB) Citations (19)
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Abstract: We suggest a new method of a probabilistic approximation of the Cauchy problem solution for the unperturbed Schrödinger equation by expectations of functionals of some random walk. In contrast to our previous papers we do not suppose the existence of exponential moment for each step of the random walk.
Key words and phrases: limit theorem, random walk, Schrödinger equation, Feynman measure.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Russian Foundation for Basic Research 16-01-00258
15-01-01453
16-01-00443
Saint Petersburg State University 11.38.263.2014
Received: 17.10.2016
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 229, Issue 6, Pages 702–713
DOI: https://doi.org/10.1007/s10958-018-3709-0
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
Citation: I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “On a limit theorem related to probabilistic representation of the Cauchy problem solution for the Schrödinger equation”, Probability and statistics. Part 24, Zap. Nauchn. Sem. POMI, 454, POMI, St. Petersburg, 2016, 158–175; J. Math. Sci. (N. Y.), 229:6 (2018), 702–713
Citation in format AMSBIB
\Bibitem{IbrSmoFad16}
\by I.~A.~Ibragimov, N.~V.~Smorodina, M.~M.~Faddeev
\paper On a~limit theorem related to probabilistic representation of the Cauchy problem solution for the Schr\"odinger equation
\inbook Probability and statistics. Part~24
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 454
\pages 158--175
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6390}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3602407}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 229
\issue 6
\pages 702--713
\crossref{https://doi.org/10.1007/s10958-018-3709-0}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042225288}
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  • https://www.mathnet.ru/eng/znsl/v454/p158
    • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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