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Zapiski Nauchnykh Seminarov POMI, 2023, Volume 526, Pages 17–28 (Mi znsl7377)  
Probabilistic approximation of the Schrödinger equation by complex-valued random processes

I. A. Alexeeva, M. V. Platonovaab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Saint Petersburg State University
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Abstract: A method for probabilistic approximation of the solution of the Cauchy problem for a one-dimensional unperturbed Schrödinger equation by mathematical expectations of functionals of some complex-valued Lévy process is proposed. In contrast to previous papers, we obtain the convergence rate of the constructed approximation to the exact solution for a wider class of initial functions.
Key words and phrases: stable distributions, Schrödinger equation, probabilistic approximation.
Funding agency Grant number
Russian Science Foundation 22-21-00016
Nonprofit foundation for support of young scientists "Möbius Contest"
Received: 14.09.2023
Document Type: Article
UDC: 519.2
Language: Russian
Citation: I. A. Alexeev, M. V. Platonova, “Probabilistic approximation of the Schrödinger equation by complex-valued random processes”, Probability and statistics. Part 35, Zap. Nauchn. Sem. POMI, 526, POMI, St. Petersburg, 2023, 17–28
Citation in format AMSBIB
\Bibitem{AlePla23}
\by I.~A.~Alexeev, M.~V.~Platonova
\paper Probabilistic approximation of the Schr\"odinger equation by complex-valued random processes
\inbook Probability and statistics. Part~35
\serial Zap. Nauchn. Sem. POMI
\yr 2023
\vol 526
\pages 17--28
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7377}
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