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2014 Multidimensional fractional advection-dispersion equations and related stochastic processes
Mirko D'Ovidio, Roberto Garra
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Electron. J. Probab. 19: 1-31 (2014). DOI: 10.1214/EJP.v19-2854

Abstract

In this paper we study multidimensional fractional advection-dispersion equations involving fractional directional derivatives both from a deterministic and a stochastic point of view. For such equations we show the connection with a class of multidimensional Lévy processes. We introduce a novel Lévy-Khinchine formula involving fractional gradients and study the corresponding infinitesimal generator of multi-dimensional random processes. We also consider more general fractional transport equations involving Frobenius-Perron operators and their stochastic solutions. Finally, some results about fractional power of second order directional derivatives and their applications are also provided.

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Mirko D'Ovidio. Roberto Garra. "Multidimensional fractional advection-dispersion equations and related stochastic processes." Electron. J. Probab. 19 1 - 31, 2014. https://doi.org/10.1214/EJP.v19-2854

Information

Accepted: 12 July 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1339.60086
MathSciNet: MR3238781
Digital Object Identifier: 10.1214/EJP.v19-2854

Subjects:
Primary: 60J35
Secondary: 35R11 , 60J70

Keywords: directional derivatives , fractional advection equation , Fractional vector calculus

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Vol.19 • 2014
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