Asymptotic behavior of semistable Lévy exponents and applications to fractal path properties

DOI10.1007/s10959-016-0720-6zbMath1387.60030arXiv1606.08490OpenAlexW3106448185MaRDI QIDQ1745280

Yimin Xiao, Mark M. Meerschaert, Peter Becker-Kern

Publication date: 20 April 2018

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.08490

zbMATH Keywords

graphHausdorff dimensionrecurrencepacking dimensiontransiencerangeLévy exponentmultiple pointssemi-selfsimilarityoperator semistable process

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Characteristic functions; other transforms (60E10) Sample path properties (60G17) Self-similar stochastic processes (60G18) Fractals (28A80) Stable stochastic processes (60G52) Hausdorff and packing measures (28A78)

Related Items (4)

On self-similar Bernstein functions and corresponding generalized fractional derivatives ⋮ On the carrying dimension of occupation measures for self-affine random fields ⋮ Space-time duality for semi-fractional diffusions ⋮ Multiple points of operator semistable Lévy processes

Cites Work

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• On the double points of operator stable Lévy processes
• Hausdorff dimension of the graph of an operator semistable Lévy process
• A dimension theorem for sample functions of stable processes
• Harmonic analysis of additive Lévy processes
• Hausdorff-Besicovitch dimension of graphs and \(p\)-variation of some Lévy processes
• Semi-selfsimilar processes
• Measuring the range of an additive Lévy process
• Hausdorff dimension of operator stable sample paths
• Group self-similar stable processes in \(\mathbb R^d\)
• Lévy processes: capacity and Hausdorff dimension
• The dimension of the set of zeros and the graph of a symmetric stable process
• Recurrence and transience of operator semi-stable processes
• The Hausdorff dimension of operator semistable Lévy processes
• Hausdorff dimension of the contours of symmetric additive Lévy processes
• Dimension results for sample paths of operator stable Lévy processes
• A dimension theorem for sample functions of processes with stable components
• Packing dimension of the range of a Lévy process
• Operator-Semistable Distributions on ${\bf R}^d$
• Operator semistable probability measures on a Hilbert space
• Operator semistable probability measures on $R^N$
• Semi-stable probability measures on $R^{N}$
• Criteria for recurrence and transience of semistable processes
• Anisotropic fractional diffusion tensor imaging
• Sample path properties of processes with stable components

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