Bernoulli

Hausdorff–Besicovitch dimension of graphs and $p$-variation of some Lévy processes

Martynas Manstavičius

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Abstract

The connection between Hausdorff–Besicovitch dimension of graphs of trajectories and various Blumenthal–Getoor indices is well known for $α$-stable Lévy processes as well as for some stationary Gaussian processes possessing Orey index. We show that the same relationship holds for several classes of Lévy processes that are popular in financial mathematics models – in particular, the Carr–Geman–Madan–Yor, normal inverse Gaussian, generalized hyperbolic, generalized $z$ and Meixner processes.

Article information

Source
Bernoulli, Volume 13, Number 1 (2007), 40-53.

Dates
First available in Project Euclid: 30 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1175287719

Digital Object Identifier
doi:10.3150/07-BEJ5121

Mathematical Reviews number (MathSciNet)
MR2307393

Zentralblatt MATH identifier
1132.60040

Keywords
Blumenthal–Getoor indices Carr–Geman–Madan–Yor process generalized hyperbolic process generalized z-process graph Hausdorff–Besicovitch dimension Lévy process Meixner process normal inverse Gaussian process p-variation

Citation

Manstavičius, Martynas. Hausdorff–Besicovitch dimension of graphs and $p$-variation of some Lévy processes. Bernoulli 13 (2007), no. 1, 40--53. doi:10.3150/07-BEJ5121. https://projecteuclid.org/euclid.bj/1175287719


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