Passage times of random walks and Lévy processes across power law boundaries

DOI10.1007/s00440-004-0414-3zbMath1082.60037OpenAlexW2051119688MaRDI QIDQ2570834

Ronald Arthur Doney, Ross A. Maller

Publication date: 28 October 2005

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

Full work available at URL: http://eprints.maths.manchester.ac.uk/901/1/Passage_Times.pdf

zbMATH Keywords

first passage time

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Stationary stochastic processes (60G10) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Brownian motion (60J65) Stopping times; optimal stopping problems; gambling theory (60G40) Sample path properties (60G17) Renewal theory (60K05)

Related Items (7)

Curve crossing for random walks reflected at their maximum ⋮ The first passage time problem over a moving boundary for asymptotically stable Lévy processes ⋮ Pruitt's estimates in Banach space ⋮ Small-time compactness and convergence behavior of deterministically and self-normalised Lévy processes ⋮ Passage of Lévy processes across power law boundaries at small times ⋮ Renewal theorems and stability for the reflected process ⋮ A lifetime of excursions through random walks and Lévy processes

Cites Work

• Dominated variation and related concepts and Tauberian theorems for Laplace transforms
• The lower limit of a normalized random walk
• Moments of passage times for Lévy processes
• Stability and attraction to normality for Lévy processes at zero and at infinity
• Stochastic bounds for Lévy processes.
• The Strong Law of Large Numbers When the Mean is Undefined
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