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Teoriya Veroyatnostei i ee Primeneniya, 2017, Volume 62, Issue 3, Pages 446–467
DOI: https://doi.org/10.4213/tvp5121 (Mi tvp5121) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Initial-boundary value problems in a bounded domain: probabilistic representations of solutions and limit theorems. II

I. A. Ibragimovab, N. V. Smorodinaba, M. M. Faddeeva

a Saint Petersburg State University
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
Full-text PDF (574 kB) Citations (5)
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DOI: https://doi.org/10.4213/tvp5121
Abstract: The paper puts forward a new method of construction of a probabilistic representation of solutions to initial-boundary value problems for a number of evolution equations (in particular, for the Schrödinger equation) in a bounded subdomain of $\mathbb R^2$ with smooth boundary. Our method is based on the construction of a special extension of the initial function from the domain to the entire plane. For problems with Neumann boundary condition, this method produces a new approach to the construction of a Wiener process “reflected from the boundary,” which was first introduced by A. V. Skorokhod.
Keywords: initial-boundary value problems, evolution equations, Schrödinger equation, limit theorems, Skorokhod problem, Feynman integral, Feynman measure.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00258
15-01-01453
16-01-00443
Russian Academy of Sciences - Federal Agency for Scientific Organizations
The first author was supported by the “Contemporary Problems of Theoretical Mathematics” program of the Division of Mathematical Sciences of the Russian Academy of Sciences and by the Russian Foundation for Basic Research (grant 16-01-00258). The second author was supported by the “Contemporary Problems of Theoretical Mathematics” program of the Division of Mathematical Sciences of the Russian Academy of Sciences and by the Russian Foundation for Basic Research (grant 15-01-01453). The third author was supported by the Russian Foundation for Basic Research (grant 16-01-00443).
Received: 06.02.2017
Accepted: 20.02.2017
English version:
Theory of Probability and its Applications, 2018, Volume 62, Issue 3, Pages 356–372
DOI: https://doi.org/10.1137/S0040585X97T98868X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “Initial-boundary value problems in a bounded domain: probabilistic representations of solutions and limit theorems. II”, Teor. Veroyatnost. i Primenen., 62:3 (2017), 446–467; Theory Probab. Appl., 62:3 (2018), 356–372
Citation in format AMSBIB
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    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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