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On Fully Mixed and Multidimensional Extensions of the Caputo and Riemann-Liouville Derivatives, Related Markov Processes and Fractional Differential Equationsстатья
Статья опубликована в высокорейтинговом журнале
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 27 октября 2021 г.
- Автор: Kolokoltsov V.
- Журнал: Fractional Calculus and Applied Analysis
- Том: 18
- Номер: 4
- Год издания: 2015
- Первая страница: 1039
- Последняя страница: 1073
- DOI: 10.1515/fca-2015-0060
- Аннотация: From the point of view of stochastic analysis the Caputo and Riemann- Liouville derivatives of order α ε (0, 2) can be viewed as (regularized) generators of stable Lévy motions interrupted on crossing a boundary. This interpretation naturally suggests fully mixed, two-sided or even multidimensional generalizations of these derivatives, as well as a probabilistic approach to the analysis of the related equations. These extensions are introduced and some well-posedness results are obtained that generalize, simplify and unify lots of known facts. This probabilistic analysis leads one to study a class of Markov processes that can be constructed from any given Markov process in Rd by blocking (or interrupting) the jumps that attempt to cross certain closed set of ’check-points’. © 2015 Diogenes Co., Sofia - frontmatter and editorial 2015.
- Добавил в систему: Колокольцов Василий Никитич