Method of calculating densities for isotropic Lévy Walks

Abstract

We provide explicit formulas for asymptotic densities of $d$-dimensional isotropic Lévy walks, when $d>1$. The densities of multidimensional undershooting and overshooting Lévy walks are presented as well. Interestingly, when the number of dimensions is odd the densities of all these Lévy walks are given by elementary functions. When $d$ is even, we can express the densities as fractional derivatives of hypergeometric functions, which makes an efficient numerical evaluation possible.

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Cited by in corpus (4)

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• Limit theorems for Lévy walks in $d$ dimensions: rare and bulk fluctuations
• Asymptotic densities of planar Lévy walks: a non-isotropic case