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Zapiski Nauchnykh Seminarov POMI, 2023, Volume 525, Pages 96–108 (Mi znsl7370)  
An analogue of the Feynman–Kac formula for the multidimensional Shrödinger equation

M. V. Platonovaab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics
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Abstract: A probabilistic approximation of the solution of the Cauchy problem for the multidimensional Schrödinger equation with limited potential is constructed. The approximation has the form of expectations of functionals of a random point field.
Key words and phrases: Schrödinger equation, Poisson random measure, Feynman–Kac formula.
Funding agency Grant number
Russian Science Foundation 22-21-00016
Received: 04.10.2023
Document Type: Article
MSC: 28C20, 60H05, 60G57
Language: Russian
Citation: M. V. Platonova, “An analogue of the Feynman–Kac formula for the multidimensional Shrödinger equation”, Probability and statistics. Part 34, Zap. Nauchn. Sem. POMI, 525, POMI, St. Petersburg, 2023, 96–108
Citation in format AMSBIB
\Bibitem{Pla23}
\by M.~V.~Platonova
\paper An analogue of the Feynman–Kac formula for the multidimensional Shr\"odinger equation
\inbook Probability and statistics. Part~34
\serial Zap. Nauchn. Sem. POMI
\yr 2023
\vol 525
\pages 96--108
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7370}
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