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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, Volume 27, Number 4, Pages 74–87
DOI: https://doi.org/10.21538/0134-4889-2021-27-4-74-87
(Mi timm1864)
 

This article is cited in 1 scientific paper (total in 1 paper)

Semigroups of operators related to stochastic processes in an extension of the Gelfand-Shilov classification

I. V. Mel'nikova, V. A. Bovkun

Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
Full-text PDF (262 kB) Citations (1)
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Abstract: Semigroups of operators corresponding to stochastic Levy processes are considered, and their connection with pseudo-differential $(\Psi D)$ operators is studied. It is shown that the semigroup generators are $\Psi D$-operators and operators with kernels from the space of slowly growing distributions. A classification of Cauchy problems is constructed for equations with operators from a special class of $\Psi D$-operators with polynomially bounded symbols. The constructed classification extends the Gelfand–Shilov classification for differential systems. In the extended classification, Cauchy problems with generators corresponding to Levy processes are well-posed in the sense of Petrovskii.
Keywords: Levy process, transition probability, semigroup of operators, pseudo-differential operator, Levy–Khintchine formula.
Received: 27.02.2021
Revised: 01.09.2021
Accepted: 06.09.2021
Bibliographic databases:
Document Type: Article
UDC: 519.21+517.983+517.982.4
Language: Russian
Citation: I. V. Mel'nikova, V. A. Bovkun, “Semigroups of operators related to stochastic processes in an extension of the Gelfand-Shilov classification”, Trudy Inst. Mat. i Mekh. UrO RAN, 27, no. 4, 2021, 74–87
Citation in format AMSBIB
\Bibitem{MelBov21}
\by I.~V.~Mel'nikova, V.~A.~Bovkun
\paper Semigroups of operators related to stochastic processes in an extension of the Gelfand-Shilov classification
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2021
\vol 27
\issue 4
\pages 74--87
\mathnet{http://mi.mathnet.ru/timm1864}
\crossref{https://doi.org/10.21538/0134-4889-2021-27-4-74-87}
\elib{https://elibrary.ru/item.asp?id=47228418}
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  • This publication is cited in the following 1 articles:
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    Trudy Instituta Matematiki i Mekhaniki UrO RAN
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