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Fractional Equations for the Scaling Limits of L’evy Walks With Position Depending Jump Distributionsстатья
Статья опубликована в высокорейтинговом журнале
Информация о цитировании статьи получена из
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 17 апреля 2024 г.
- Автор: Kolokoltsov V.N.
- Журнал: Mathematics
- Том: 11
- Год издания: 2023
- Издательство: MDPI
- Местоположение издательства: Basel, Switzerland
- Номер статьи: 2566
- DOI: 10.3390/math11112566
- Аннотация: L\'evy walks represent important modeling tools for variety of real life processes. Their natural scaling limits are known to be described by the so-called material fractional derivatives. So far these scaling limits were derived for spatially homogeneous walks, where Fourier and Laplace transforms represent natural tools of analysis.Here we derive the corresponding limiting equations in the case of position depending times and velocities of walks, where Fourier transforms cannot be effectively applied. In fact, we derive three different limits (specified by the way the process is stopped at an attempt to cross the boundary),leading to three different multi-dimensional versions of Caputo-Dzherbashian derivatives, which correspond to different boundary conditions for the generators of the related Feller semigroups and processes. Some other extensions and generalisations are analysed.
- Добавил в систему: Колокольцов Василий Никитич