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Teoriya Veroyatnostei i ee Primeneniya, 2022, Volume 67, Issue 1, Pages 23–36
DOI: https://doi.org/10.4213/tvp5368 (Mi tvp5368) 		 
Reflecting Lévy processes and associated families of linear operators. II

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
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DOI: https://doi.org/10.4213/tvp5368
Abstract: We consider special one-dimensional Markov processes, namely, asymmetric jump Lévy processes, which have values in a given interval and reflect from the boundary points. We show that in this case, 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. This study is a continuation of our paper [Theory Probab.Appl., 64 (2019), 335–354], where a similar problem was solved for symmetric reflecting Lévy processes.
Keywords: random processes, initial-boundary problems, limit theorems, local time.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00657
The work of M. M. Faddeev was supported by the Russian Foundation for Basic Research (project 19-01-00657).
Received: 18.10.2019
Accepted: 23.07.2020
English version:
Theory of Probability and its Applications, 2022, Volume 67, Issue 1, Pages 17–27
DOI: https://doi.org/10.1137/S0040585X97T990721
Bibliographic databases:
Document Type: Article
MSC: 28C20, 60H05, 60G57
Language: Russian
Citation: I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “Reflecting Lévy processes and associated families of linear operators. II”, Teor. Veroyatnost. i Primenen., 67:1 (2022), 23–36; Theory Probab. Appl., 67:1 (2022), 17–27
Citation in format AMSBIB
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\by I.~A.~Ibragimov, N.~V.~Smorodina, M.~M.~Faddeev
\paper Reflecting L\'evy processes and associated families of linear operators.~II
\jour Teor. Veroyatnost. i Primenen.
\yr 2022
\vol 67
\issue 1
\pages 23--36
\mathnet{http://mi.mathnet.ru/tvp5368}
\crossref{https://doi.org/10.4213/tvp5368}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4466410}
\zmath{https://zbmath.org/?q=an:7523556}
\transl
\jour Theory Probab. Appl.
\yr 2022
\vol 67
\issue 1
\pages 17--27
\crossref{https://doi.org/10.1137/S0040585X97T990721}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85130994615}
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