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On fully mixed and multidimensional extensions of the Caputo and Riemann-Liouville derivatives, related Markov processes and fractional differential equations
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Kolokoltsov, V. N. (Vasiliĭ Nikitich) (2015) On fully mixed and multidimensional extensions of the Caputo and Riemann-Liouville derivatives, related Markov processes and fractional differential equations. Fractional Calculus and Applied Analysis, 18 (4). pp. 1039-1073. doi:10.1515/fca-2015-0060 ISSN 1311-0454.
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Official URL: http://dx.doi.org/10.1515/fca-2015-0060
Abstract
From the point of view of stochastic analysis the Caputo and Riemann- Liouville derivatives of order α ∈ (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’.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Journal or Publication Title: | Fractional Calculus and Applied Analysis | ||||||
Publisher: | Bulgarian Academy of Sciences, Institute of Mathematics and Informatics | ||||||
ISSN: | 1311-0454 | ||||||
Official Date: | 4 August 2015 | ||||||
Dates: |
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Volume: | 18 | ||||||
Number: | 4 | ||||||
Page Range: | pp. 1039-1073 | ||||||
DOI: | 10.1515/fca-2015-0060 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
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