Dimension results for sample paths of operator stable Lévy processes

DOI10.1016/j.spa.2004.08.004zbMath1074.60079OpenAlexW2054803000MaRDI QIDQ2485816

Mark M. Meerschaert, Yimin Xiao

Publication date: 5 August 2005

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2004.08.004

zbMATH Keywords

Hausdorff dimensionpacking dimensionrangeoperator stable processes

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Continuous-time Markov processes on general state spaces (60J25) Sample path properties (60G17) Fractals (28A80)

Related Items (16)

Sample Path Properties of a Class of Operator Stable Processes ⋮ Modeling and simulation with operator scaling ⋮ Hausdorff measure and packing measure of the graph of dilation-stable Lévy processes ⋮ Packing dimension of the range of a Lévy process ⋮ On the carrying dimension of occupation measures for self-affine random fields ⋮ Fractal dimension results for continuous time random walks ⋮ Multifractal properties of sample paths of ground state-transformed jump processes ⋮ The Hausdorff dimension of the range of the Lévy multistable processes ⋮ Asymptotic behavior of semistable Lévy exponents and applications to fractal path properties ⋮ Fractal sets determined by dilation-stable processes ⋮ The Hausdorff dimension of operator semistable Lévy processes ⋮ On the double points of operator stable Lévy processes ⋮ Laws of the iterated logarithm of chover-type for operator stable Lévy processes ⋮ Space-time duality for semi-fractional diffusions ⋮ Multiple points of operator semistable Lévy processes ⋮ Hausdorff dimension, heavy tails, and generalization in neural networks*

Cites Work

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• Operator-Self-Similar Processes in a Finite-Dimensional Space
• Sample path properties of processes with stable components
• Hausdorff Dimension in a Process with Stable Components--An Interesting Counterexample
• The horizon problem for random surfaces
• Regularly varying functions
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