Escape rates for multidimensional shift self-similar additive sequences

DOI10.1007/s10959-015-0599-7zbMath1354.60040arXiv1403.0696OpenAlexW2090261093MaRDI QIDQ325903

Toshiro Watanabe

Publication date: 11 October 2016

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

Full work available at URL: https://arxiv.org/abs/1403.0696

zbMATH Keywords

law of iterated logarithmBrownian motions\(b\)-decomposable distributionshift self-similar additive sequencestationary OU-type sequencestrictly stable Lévy process

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Stationary stochastic processes (60G10) Strong limit theorems (60F15) Brownian motion (60J65) Self-similar stochastic processes (60G18) Stable stochastic processes (60G52)

Cites Work

• The occupation time of Brownian motion in a ball
• The rate of escape of random walk
• The Brownian escape process
• Semi-selfsimilar processes
• On the future infima of some transient processes
• Nested classes of \(C\)-decomposable laws
• Self-similar processes with independent increments associated with Lévy and Bessel processes.
• Limit theorems for shift selfsimilar additive random sequences
• Shift self-similar additive random sequences associated with supercritical branching processes
• Semi-Lévy processes, semi-selfsimilar additive processes, and semi-stationary Ornstein-Uhlen\-beck type processes
• Sample function behavior of increasing processes of class \(L\)
• Self-similar processes with independent increments
• Exact Hausdorff measure on the boundary of a Galton-Watson tree
• Limsup behaviors of multi-dimensional selfsimilar processes with independent increments
• Some Theorems Concerning 2-Dimensional Brownian Motion
• Exact Packing Measure on the Boundary of a Galton–Watson Tree
• Spitzer's test for the cauchy process on the line
• Continuity properties of distributions with some decomposability
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