Geodesic
On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes
Fractional calculus and applied analysis, Tome 8 (2005) no. 1, pp. 73-88.

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In this paper the multi-dimensional analog of the Gillis-Weiss random walk model is studied. The convergence of this random walk to a fractional diffusion process governed by a symmetric operator defined as a hypersingular integral or the inverse of the Riesz potential in the sense of distributions is proved.
Keywords: Multi-Dimensional Random Walk, Cauchy Problem, Fractional Diffusion Equation, Pseudo-Differential Operators, Fundamental Solution, Hypersingular Integral, 26A33, 47B06, 47G30, 60G50, 60G52, 60G60 
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Umarov, Sabir; Gorenflo, Rudolf. On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes. Fractional calculus and applied analysis, Tome 8 (2005) no. 1, pp. 73-88. http://geodesic.mathdoc.fr/item/FCAA_2005_8_1_a4/