@article{EJP2854,
author = {Mirko D'Ovidio and Roberto Garra},
title = {Multidimensional fractional advection-dispersion equations and related stochastic processes},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {19},
year = {2014},
keywords = {Fractional vector calculus; directional derivatives; fractional advection equation},
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.},
pages = {no. 61, 1-31},
issn = {1083-6489},
doi = {10.1214/EJP.v19-2854},
url = {http://ejp.ejpecp.org/article/view/2854}}