- Volume 13, Number 1 (2007), 40-53.
Hausdorff–Besicovitch dimension of graphs and $p$-variation of some Lévy processes
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.
Bernoulli, Volume 13, Number 1 (2007), 40-53.
First available in Project Euclid: 30 March 2007
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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
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