An almost sure functional limit theorem at zero for a class of Lévy processes normed by the square root function, and applications

DOI10.1007/s00440-007-0103-0zbMath1153.60025OpenAlexW2157737860MaRDI QIDQ948941

Alex Szimayer, Boris Buchmann, Ross A. Maller

Publication date: 16 October 2008

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00440-007-0103-0

zbMATH Keywords

almost sure convergencelocal behaviourLevy processes

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17)

Related Items

Moderate deviations and Strassen's law for additive processes ⋮ Small-time compactness and convergence behavior of deterministically and self-normalised Lévy processes ⋮ The small-time Chung-Wichura law for Lévy processes with non-vanishing Brownian component ⋮ Small time two-sided LIL behavior for Lévy processes at zero ⋮ LIL type behavior of multivariate Lévy processes at zero

Cites Work

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• An inversion of Strassen's law of the iterated logarithm for small time
• Large deviations and functional iterated logarithm law for diffusion processes
• Strassen's law of the iterated logarithm for diffusion processes for small time
• Small deviations in the functional central limit theorem with applications to functional laws of the iterated logarithm
• Passage of Lévy processes across power law boundaries at small times
• A relation between Chung's and Strassen's laws of the iterated logarithm
• A joint functional law for the Wiener process and principal value
• An invariance principle for the law of the iterated logarithm
• The Law of the Iterated Logarithm for Empirical Distribution
• The Limit Points of a Normalized Random Walk