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 Zap. Nauchn. Sem. POMI, 2017, Volume 466, Pages 257–272 (Mi znsl6553)

A probabilistic approximation of the Cauchy problem solution for the Schrödinger equation with a fractional derivative operator

M. V. Platonovaab, S. V. Tsykinc

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics, St. Petersburg, Russia
c St. Petersburg State University, St. Petersburg, Russia

Abstract: We construct two types of probabilistic approximations of the Cauchy problem solution for the nonstationary Schrödinger equation with a symmetric fractional derivative of order $\alpha\in(1,2)$ on the right hand side. In the first case we approximate the solution by a mathematical expectation of point Poisson field functionals and in the second case we approximate the solution by a mathematical expectation of functionals of sums of independent random variables with a power asymptotics of a tail distribution.

Key words and phrases: fractional derivative, Schroedinger equation, limit theorem, point Poisson field.

 Funding Agency Grant Number Russian Science Foundation 17-11-01136 Russian Foundation for Basic Research 16-01-00443à

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Document Type: Article
UDC: 519,21

Citation: M. V. Platonova, S. V. Tsykin, “A probabilistic approximation of the Cauchy problem solution for the Schrödinger equation with a fractional derivative operator”, Probability and statistics. Part 26, Zap. Nauchn. Sem. POMI, 466, POMI, St. Petersburg, 2017, 257–272

Citation in format AMSBIB
\Bibitem{PlaTsy17} \by M.~V.~Platonova, S.~V.~Tsykin \paper A probabilistic approximation of the Cauchy problem solution for the Schr\"odinger equation with a~fractional derivative operator \inbook Probability and statistics. Part~26 \serial Zap. Nauchn. Sem. POMI \yr 2017 \vol 466 \pages 257--272 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6553}