Stability of the overshoot for Lévy processes

DOI10.1214/aop/1020107765zbMath1016.60052OpenAlexW2057764228MaRDI QIDQ1872256

Ronald Arthur Doney, Ross A. Maller

Publication date: 6 May 2003

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

Full work available at URL: https://doi.org/10.1214/aop/1020107765

zbMATH Keywords

Lévy processesfirst passage timeslocal behaviourexit timesindependent incrementsexit systemsLévy characteristics

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Sample path properties (60G17)

Related Items (22)

Stochastic bounds for Lévy processes. ⋮ Stability of the exit time for Lévy processes ⋮ The maximum of a Lévy process reflected at a general barrier ⋮ Compactness and continuity properties for a Lévy process at a two-sided exit time ⋮ Stability of overshoots of Markov additive processes ⋮ Asymptotic distributions of the overshoot and undershoots for the Lévy insurance risk process in the Cramér and convolution equivalent cases ⋮ Small-time compactness and convergence behavior of deterministically and self-normalised Lévy processes ⋮ Passage of Lévy processes across power law boundaries at small times ⋮ On the ladder heights of random walks attracted to stable laws of exponent 1 ⋮ Small time one-sided LIL behavior for Lévy processes at zero ⋮ Exact and asymptotic \(n\)-tuple laws at first and last passage ⋮ Asymptotic results for time-changed Lévy processes sampled at hitting times ⋮ A note on summability of ladder heights and the distributions of ladder epochs for random walks ⋮ Asymptotic behavior of the hitting time, overshoot and undershoot for some Lévy processes ⋮ Weak convergence of positive self-similar Markov processes and overshoots of Lévy processes ⋮ Distributional representations and dominance of a Lévy process over its maximal jump processes ⋮ On exact sampling of the first passage event of a Lévy process with infinite Lévy measure and bounded variation ⋮ Renewal theorems and stability for the reflected process ⋮ A lifetime of excursions through random walks and Lévy processes ⋮ Finiteness of integrals of functions of Lévy processes ⋮ Windings of Planar Stable Processes ⋮ A necessary and sufficient condition for the convergence of the derivative martingale in a branching Lévy process

Cites Work

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• The growth of random walks and Levy processes
• On the position of a random walk at the time of first exit from a sphere
• Cramér's estimate for Lévy processes
• Regularity of the half-line for Lévy processes
• Stability and attraction to normality for Lévy processes at zero and at infinity
• \(L^ p\)-boundedness of the overshoot in multidimensional renewal theory
• Exit Properties of Stochastic Processes with Stationary Independent Increments
• On the rate of growth of the overshoot and the maximum partial sum
• On Distributions of Functionals Related to Boundary Problems for Processes with Independent Increments
• A convolution equation and hitting probabilities of single points for processes with stationary independent increments
• The Limit Points of a Normalized Random Walk

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