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- W2024158500 abstract "Let ${X(t)}_{tge 0}$ denote a Lévy process in ${mathbf {R}}^d$ with exponent $Psi$. Taylor (1986) proved that the packing dimension of the range $X([0 ,1])$ is given by the index begin{equation*} {(0.1)}qquad qquad gamma â = sup left {alpha ge 0: liminf _{r to 0^+} int _0^1 frac {mathrm {P} left {|X(t)| le rright }}{r^alpha } dt =0right }.qquad qquad end{equation*} We provide an alternative formulation of $gamma â$ in terms of the Lévy exponent $Psi$. Our formulation, as well as methods, are Fourier-analytic, and rely on the properties of the Cauchy transform. We show, through examples, some applications of our formula." @default.
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- W2024158500 date "2008-03-04" @default.
- W2024158500 modified "2023-09-26" @default.
- W2024158500 title "Packing dimension of the range of a Lévy process" @default.
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- W2024158500 doi "https://doi.org/10.1090/s0002-9939-08-09163-6" @default.
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