Small time two-sided LIL behavior for Lévy processes at zero

DOI10.1007/s00440-008-0142-1zbMath1163.60020OpenAlexW2028990728MaRDI QIDQ1017897

Mladen Svetoslavov Savov

Publication date: 13 May 2009

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

Full work available at URL: https://doi.org/10.1007/s00440-008-0142-1

zbMATH Keywords

Lévy processLIL behaviornorming functions

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Strong limit theorems (60F15)

Related Items (10)

Upper functions for sample paths of Lévy(-type) processes ⋮ On the small-time behaviour of Lévy-type processes ⋮ Short-time behavior of solutions to Lévy-driven stochastic differential equations ⋮ How smooth can the convex hull of a Lévy path be? ⋮ Small time Chung-type LIL for Lévy processes ⋮ Probabilistic analysis of the single particle Wigner Monte-Carlo method ⋮ The small-time Chung-Wichura law for Lévy processes with non-vanishing Brownian component ⋮ Semi-Markov processes, integro-differential equations and anomalous diffusion-aggregation ⋮ Ruin and deficit under claim arrivals with the order statistics property ⋮ LIL type behavior of multivariate Lévy processes at zero

Cites Work

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• Fluctuation theory for Lévy processes. Ecole d'Eté de probabilités de Saint-Flour XXXV -- 2005.
• An almost sure functional limit theorem at zero for a class of Lévy processes normed by the square root function, and applications
• Passage of Lévy processes across power law boundaries at small times
• Some results on two-sided LIL behavior
• Small-time versions of Strassen's law for Lévy processes
• Toward a universal law of the iterated logarithm
• Toward a universal law of the iterated logarithm, Part II
• The 1971 Rietz Lecture Sums of Independent Random Variables--Without Moment Conditions

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