|
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
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
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
Linking options:
https://www.mathnet.ru/eng/timm1864 https://www.mathnet.ru/eng/timm/v27/i4/p74
|
Statistics & downloads: |
Abstract page: | 134 | Full-text PDF : | 33 | References: | 22 | First page: | 6 |
|