Small deviations of general Lévy processes

DOI10.1214/09-AOP457zbMath1187.60035arXiv0805.1330OpenAlexW2063992100MaRDI QIDQ1035870

Steffen Dereich, Frank Aurzada

Publication date: 4 November 2009

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0805.1330

zbMATH Keywords

Lévy processEsscher transformsmall deviationslower tail probabilitysmall ball problem

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Limit theorems in probability theory (60F99)

Related Items (12)

Proper two-sided exits of a Lévy process ⋮ Existence of a density of the 2-dimensional stochastic Navier Stokes equation driven by Lévy processes or fractional Brownian motion ⋮ A constructive sharp approach to functional quantization of stochastic processes ⋮ Moment bounds for a generalized Anderson model with Gaussian noise rough in space ⋮ Small time Chung-type LIL for Lévy processes ⋮ Reviewing alternative characterizations of Meixner process ⋮ Sticky processes, local and true martingales ⋮ On the conditional small ball property of multivariate Lévy-driven moving average processes ⋮ The small-time Chung-Wichura law for Lévy processes with non-vanishing Brownian component ⋮ Irreducibility and exponential mixing of some stochastic hydrodynamical systems driven by pure jump noise ⋮ Ergodicity of Stochastic Shell Models Driven by Pure Jump Noise ⋮ On certain integral functionals of squared Bessel processes

Cites Work

• Small ball probabilities for jump Lévy processes from the Wiener domain of attraction
• Tempering stable processes
• Metric entropy and the small ball problem for Gaussian measures
• Approximation, metric entropy and small ball estimates for Gaussian measures
• On the small deviations of a Lévy process
• Small deviations in \(p\)-variation for multidimensional Lévy processes
• Small deviations for fractional stable processes
• Evaluating the small deviation probabilities for subordinated Lévy processes
• On probabilities of small deviations for stochastic processes
• The Integral of a Symmetric Unimodal Function over a Symmetric Convex Set and Some Probability Inequalities
• Approximation and entropy numbers of Volterra operators with application to Brownian motion
• Small deviations for the Poisson process
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Small deviations of general Lévy processes