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 Lé...

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Bibliographic Details
Published in:Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2007-02, Vol.13 (1), p.40-53
Main Author: Manstavičius, Martynas
Format: Article
Language:English
Subjects:
Blumenthal–Getoor indices
Brownian motion
Carr–Geman–Madan–Yor process
Density
Eigenfunctions
Finance
generalized hyperbolic process
generalized z-process
graph
Hausdorff–Besicovitch dimension
Lebesgue measures
Lévy process
Mathematical functions
Mathematical inequalities
Mathematical theorems
Meixner process
normal inverse Gaussian process
p-variation
Trajectories
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Summary: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.
ISSN:1350-7265
DOI:10.3150/07-BEJ5121