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Teoriya Veroyatnostei i ee Primeneniya, 2019, Volume 64, Issue 3, Pages 417–441
DOI: https://doi.org/10.4213/tvp5254 (Mi tvp5254) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Reflecting Lévy processes and associated families of linear operators

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

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Saint Petersburg State University
Full-text PDF (539 kB) Citations (4)
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DOI: https://doi.org/10.4213/tvp5254
Abstract: The paper is concerned with special one-dimensional Markov processes, which are Lévy processes defined on a finite interval and reflected from the boundary points of the interval. It is shown that in this setting, in addition to the standard semigroup of operators generated by the Markov process, there also appears the family of “boundary” random operators that send functions defined on the boundary of the interval to elements of the space $L_2$ on the entire interval. In the case when the original process is a Wiener process, we show that these operators can be expressed in terms of the local time of the process on the boundary of the interval.
Keywords: random process, initial boundary value problem, limit theorem, local time.
Funding agency Grant number
Russian Science Foundation 17-11-01136
Russian Academy of Sciences - Federal Agency for Scientific Organizations PRAS-18-01
The work of the first author (section 6) was supported by the Program of the Presidium of the Russian Academy of Sciences no. 01 “Fundamental Mathematics and Its Applications” under grant PRAS-18-01. The work of the second and third authors (sections 2–5) was supported by the Russian Science Foundation (grant 17-11-01136).
Received: 10.10.2018
Accepted: 21.02.2019
English version:
Theory of Probability and its Applications, 2019, Volume 64, Issue 3, Pages 335–354
DOI: https://doi.org/10.1137/S0040585X97T989532
Bibliographic databases:
Document Type: Article
MSC: 60G51
Language: Russian
Citation: I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “Reflecting Lévy processes and associated families of linear operators”, Teor. Veroyatnost. i Primenen., 64:3 (2019), 417–441; Theory Probab. Appl., 64:3 (2019), 335–354
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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