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Funktsional'nyi Analiz i ego Prilozheniya, 2018, Volume 52, Issue 2, Pages 25–39
DOI: https://doi.org/10.4213/faa3517 (Mi faa3517) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Probabilistic Approximation of the Evolution Operator

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

a St. Petersburg Department of Steklov Mathematical Institute, Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia
Full-text PDF (247 kB) Citations (9)
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DOI: https://doi.org/10.4213/faa3517
Abstract: A method for approximation of the operator $e^{-itH}$, where $H=-\frac{1}{2}\frac{d^2}{dx^2}+V(x)$, in the strong operator topology is proposed. The approximating operators have the form of expectations of functionals of a certain random point field.
Keywords: evolution equation, limit theorem, Feynman–Kac formula.
Funding agency Grant number
Russian Science Foundation 17-11-01136
Russian Foundation for Basic Research 16-01-00258
I. A. Ibragimov acknowledges the financial support of the Russian Foundation for Basic Research (project no. 16-01-00258). N. V. Smorodina (who authors the results of Section 3) acknowledges the support of the Russian Science Foundation (project no. 17-11-01136). M. M. Faddeev (who authors the results of Section 4) acknowledges the support of the Russian Science Foundation (project no. 17-11-01136).
Received: 31.08.2017
English version:
Functional Analysis and Its Applications, 2018, Volume 52, Issue 2, Pages 101–112
DOI: https://doi.org/10.1007/s10688-018-0216-5
Bibliographic databases:
Document Type: Article
UDC: 519.2
MSC: 28C20, 60H05, 60G57
Language: Russian
Citation: I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “Probabilistic Approximation of the Evolution Operator”, Funktsional. Anal. i Prilozhen., 52:2 (2018), 25–39; Funct. Anal. Appl., 52:2 (2018), 101–112
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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