Small time Chung-type LIL for Lévy processes

DOI10.3150/11-BEJ395zbMath1270.60044arXiv1002.0675OpenAlexW2024296372MaRDI QIDQ1940751

Leif Döring, Frank Aurzada, Mladen Svetoslavov Savov

Publication date: 7 March 2013

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.0675

zbMATH Keywords

Lévy processessmall deviationslaw of the iterated logarithm (LIL)small ball problem

Mathematics Subject Classification ID

Strong limit theorems (60F15) Large deviations (60F10) Sample path properties (60G17) Right processes (60J40)

Related Items (10)

Zooming in on a Lévy process at its supremum ⋮ Intermittency in the small-time behavior of Lévy processes ⋮ On the small-time behaviour of Lévy-type processes ⋮ How smooth can the convex hull of a Lévy path be? ⋮ General Law of iterated logarithm for Markov processes: Liminf laws ⋮ A simple condition for the multivariate CLT and the attraction to the Gaussian of Lévy processes at long and short times ⋮ Semi-Markov processes, integro-differential equations and anomalous diffusion-aggregation ⋮ Ruin and deficit under claim arrivals with the order statistics property ⋮ Conditions for a Lévy process to stay positive near 0, in probability ⋮ Windings of Planar Stable Processes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The small-time Chung-Wichura law for Lévy processes with non-vanishing Brownian component
• Small ball probabilities for jump Lévy processes from the Wiener domain of attraction
• Small time two-sided LIL behavior for Lévy processes at zero
• Small deviations of general Lévy processes
• Lower functions for processes with stationary independent increments
• Lower functions for asymmetric Lévy processes
• On the small deviations of a Lévy process
• Small deviations in \(p\)-variation for multidimensional Lévy processes
• On the limiting behaviour of Lévy processes at zero
• Passage of Lévy processes across power law boundaries at small times
• Small deviations for fractional stable processes
• Evaluating the small deviation probabilities for subordinated Lévy processes
• On probabilities of small deviations for stochastic processes
• On the First Exit Time of a Completely Asymmetric Stable Process from a Finite Interval
• Lower functions for increasing random walks and subordinators
• On the Maximum Partial Sums of Sequences of Independent Random Variables

This page was built for publication: Small time Chung-type LIL for Lévy processes