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Zap. Nauchn. Sem. POMI, 2017, Volume 466, Pages 134–144 (Mi znsl6546)  

A probabilistic approximation of the evolution operator $\exp(t(S\nabla,\nabla))$ with a complex matrix $S$

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

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

Abstract: We consider some problems concerning a probabilistic interpretation of the Cauchy problem solution for the equation $\frac{\partial u}{\partial t}=\frac12(S\nabla,\nabla)u$, where $S$ is a symmetric complex matrix such that $\operatorname{Re}S\ge0$.

Key words and phrases: limit theorem, Schrödinger equation, Feynman measure, random walk, evolution equation.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00258
Russian Science Foundation 17-11-01136


Full text: PDF file (198 kB)
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Document Type: Article
UDC: 519.2
Received: 18.10.2017

Citation: I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “A probabilistic approximation of the evolution operator $\exp(t(S\nabla,\nabla))$ with a complex matrix $S$”, Probability and statistics. Part 26, Zap. Nauchn. Sem. POMI, 466, POMI, St. Petersburg, 2017, 134–144

Citation in format AMSBIB
\Bibitem{IbrSmoFad17}
\by I.~A.~Ibragimov, N.~V.~Smorodina, M.~M.~Faddeev
\paper A probabilistic approximation of the evolution operator $\exp(t(S\nabla,\nabla))$ with a~complex matrix~$S$
\inbook Probability and statistics. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 466
\pages 134--144
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6546}


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  • Записки научных семинаров ПОМИ
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