Almost sure relative stability of the overshoot of power law boundaries

DOI10.1007/S10959-006-0040-3zbMath1112.60036OpenAlexW2082286926MaRDI QIDQ877230

Ross A. Maller, Ronald Arthur Doney

Publication date: 19 April 2007

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10959-006-0040-3

zbMATH Keywords

Random walkCurved boundariesOvershoot of power-law boundaries

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Stopping times; optimal stopping problems; gambling theory (60G40) Renewal theory (60K05)

Related Items (2)

Pruitt's estimates in Banach space ⋮ A lifetime of excursions through random walks and Lévy processes

Cites Work

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• The growth of random walks and Levy processes
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• Gambler's ruin and the first exit position of random walk from large spheres
• \(L^ p\)-boundedness of the overshoot in multidimensional renewal theory
• Random walks crossing curved boundaries: a functional limit theorem, stability and asymptotic distributions for exit times and positions
• On the rate of growth of the overshoot and the maximum partial sum
• Overshoots over curved boundaries
• Overshoots over curved boundaries. II

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