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Zap. Nauchn. Sem. POMI, 2018, Volume 474, Pages 149–170 (Mi znsl6675)  

This article is cited in 1 scientific paper (total in 1 paper)

Probabilistic representations for initial-boundary value problem solutions to the non-stationary Schrödinger equation in $d$-hyperball

P. N. Ievlevab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b Saint Petersburg State University, Saint Petersburg, Russia

Abstract: We extend the construction of probabilistic representations for initial-boundary value problem solutions to the non-stationary Schrödinger equation in d-hyperball first obtained in the works by I. Ibragimov, N. Smorodina and M. Faddeev to a multidimensional case. Further on, we show that in these representations the Wiener process could be replaced by a random walk approximation. The $L_2$-convergence rates are obtained.

Key words and phrases: limit theorems, Schrodinger equation, initial-boundary value problems, evolution equations, hyperspherical Bessel functions.

Funding Agency Grant Number
Russian Science Foundation 17-11-01136


Full text: PDF file (257 kB)
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UDC: 519.2
Received: 30.10.2018

Citation: P. N. Ievlev, “Probabilistic representations for initial-boundary value problem solutions to the non-stationary Schrödinger equation in $d$-hyperball”, Probability and statistics. Part 27, Zap. Nauchn. Sem. POMI, 474, POMI, St. Petersburg, 2018, 149–170

Citation in format AMSBIB
\Bibitem{Iev18}
\by P.~N.~Ievlev
\paper Probabilistic representations for initial-boundary value problem solutions to the non-stationary Schr\" odinger equation in $d$-hyperball
\inbook Probability and statistics. Part~27
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 474
\pages 149--170
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6675}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. P. N. Ievlev, “Brounovskoe dvizhenie s otrazheniem v $d$-mernom share”, Veroyatnost i statistika. 28, Zap. nauchn. sem. POMI, 486, POMI, SPb., 2019, 158–177  mathnet
  • Записки научных семинаров ПОМИ
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