Semigroups of operators related to stochastic processes in an extension of the Gelfand–Shilov classification
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
Semigroups of operators related to stochastic processes in an extension of the Gelfand–Shilov classification
|
|
| Автор |
Melnikova, I. V.
Bovkun, V. A. |
|
| Тематика |
LEVY PROCESS
LEVY–KHINTCHINE FORMULA PSEUDO-DIFFERENTIAL OPERATOR SEMIGROUP OF OPERATORS TRANSITION PROBABILITY |
|
| Описание |
Semigroups of operators corresponding to stochastic Levy processes are considered, and their connection with pseudo-differential (ΨD) operators is studied. It is shown that the semigroup generators are ΨD-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 ΨD-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. © 2021 The authors.
|
|
| Дата |
2024-04-08T11:07:50Z
2024-04-08T11:07:50Z 2022 |
|
| Тип |
Article
Journal article (info:eu-repo/semantics/article) Published version (info:eu-repo/semantics/publishedVersion) |
|
| Идентификатор |
Мельникова, ИВ & Бовкун, ВА 2021, 'Полугруппы операторов, связанные со случайными процессами, в расширении классификации Гельфанда — Шилова', Труды института математики и механики УрО РАН, Том. 27, № 4, стр. 74-87. https://doi.org/10.21538/0134-4889-2021-27-4-74-87
Мельникова, И. В., & Бовкун, В. А. (2021). Полугруппы операторов, связанные со случайными процессами, в расширении классификации Гельфанда — Шилова. Труды института математики и механики УрО РАН, 27(4), 74-87. https://doi.org/10.21538/0134-4889-2021-27-4-74-87 0134-4889 Final All Open Access; Bronze Open Access http://journal.imm.uran.ru/sites/default/files/content/27_4/TrIMMUrORAN_2021_4_p74_L.pdf http://journal.imm.uran.ru/sites/default/files/content/27_4/TrIMMUrORAN_2021_4_p74_L.pdf http://elar.urfu.ru/handle/10995/131520 47228418 10.21538/0134-4889-2021-27-4-74-87 85142161566 000756004700006 |
|
| Язык |
ru
|
|
| Права |
Open access (info:eu-repo/semantics/openAccess)
|
|
| Формат |
application/pdf
|
|
| Издатель |
Krasovskii Institute of Mathematics and Mechanics
|
|
| Источник |
Trudy Instituta Matematiki i Mekhaniki UrO RAN
Trudy Instituta Matematiki i Mekhaniki UrO RAN |
|