Packing dimension of the range of a Lévy process
Open Access
- 4 March 2008
- journal article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 136 (07), 2597-2607
- https://doi.org/10.1090/s0002-9939-08-09163-6
Abstract
Let <!-- MATH $\{X(t)\}_{t\ge 0}$ --> denote a Lévy process in <!-- MATH ${\mathbf{R}}^d$ --> with exponent . Taylor (1986) proved that the packing dimension of the range <!-- MATH $X([0\,,1])$ --> is given by the index <!-- MATH \begin{displaymath} {(0.1)}\qquad\qquad \gamma' = \sup\left\{\alpha\ge 0: \liminf_{r \to 0^+}\, \, \int_0^1 \frac{\mathrm{P} \left\{|X(t)| \le r\right\}}{r^\alpha} \, dt =0\right\}.\qquad\qquad \end{displaymath} -->
Keywords
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