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On Fully Mixed and Multidimensional Extensions of the Caputo and Riemann-Liouville Derivatives, Related Markov Processes and Fractional Differential Equations. / Kolokoltsov, Vassili.

In: Fractional Calculus and Applied Analysis, Vol. 18, No. 4, 01.08.2015, p. 1039-1073.

Research output: Contribution to journal › Article › peer-review

Harvard

Kolokoltsov, V 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, vol. 18, no. 4, pp. 1039-1073. https://doi.org/10.1515/fca-2015-0060

APA

Kolokoltsov, V. (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), 1039-1073. https://doi.org/10.1515/fca-2015-0060

Vancouver

Kolokoltsov V. 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. 2015 Aug 1;18(4):1039-1073. https://doi.org/10.1515/fca-2015-0060

Author

Kolokoltsov, Vassili. / On Fully Mixed and Multidimensional Extensions of the Caputo and Riemann-Liouville Derivatives, Related Markov Processes and Fractional Differential Equations. In: Fractional Calculus and Applied Analysis. 2015 ; Vol. 18, No. 4. pp. 1039-1073.

BibTeX

@article{c112396bd0e54a28aa60ff8255036e7c,
title = "On Fully Mixed and Multidimensional Extensions of the Caputo and Riemann-Liouville Derivatives, Related Markov Processes and Fractional Differential Equations",
abstract = "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 L{\'e}vy 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'.",
keywords = "boundary value problem, Caputo fractional derivative, crossing a boundary, Markov processes, Riemann-Liouville fractional derivative",
author = "Vassili Kolokoltsov",
year = "2015",
month = aug,
day = "1",
doi = "10.1515/fca-2015-0060",
language = "English",
volume = "18",
pages = "1039--1073",
journal = "Fractional Calculus and Applied Analysis",
issn = "1311-0454",
publisher = "De Gruyter",
number = "4",

}

RIS

TY - JOUR

T1 - On Fully Mixed and Multidimensional Extensions of the Caputo and Riemann-Liouville Derivatives, Related Markov Processes and Fractional Differential Equations

AU - Kolokoltsov, Vassili

PY - 2015/8/1

Y1 - 2015/8/1

N2 - 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'.

AB - 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'.

KW - boundary value problem

KW - Caputo fractional derivative

KW - crossing a boundary

KW - Markov processes

KW - Riemann-Liouville fractional derivative

UR - http://www.scopus.com/inward/record.url?scp=84939188218&partnerID=8YFLogxK

U2 - 10.1515/fca-2015-0060

DO - 10.1515/fca-2015-0060

M3 - Article

AN - SCOPUS:84939188218

VL - 18

SP - 1039

EP - 1073

JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

SN - 1311-0454

IS - 4

ER -

ID: 51531301