Convergence rates for record times and the associated counting process

DOI10.1016/0304-4149(90)90047-VzbMath0709.60018MaRDI QIDQ921703

Allan Gut

Publication date: 1990

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

rate of convergencecentral limit theoremcounting processrecord times

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Stochastic processes (60G99) (L^p)-limit theorems (60F25)

Related Items

Limit theorems for counting variables based on records and extremes, On record indices and record times, Strong approximation of the number of renewal paced record times, On the number of boundary crossings related to LIL and SLLN for record values and partial maxima of i.i.d. sequences and extremes of uniform spacings, Precise asymptotics in complete moment convergence of the associated counting process, A Note on Rényi's ‘Record’ Problem and Engel's Series, Precise asymptotics for record times and the associated counting process.

Cites Work

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• Almost sure limit points of and the number of boundary crossings related to SLLN and LIL for record times, inter-record times and the number of record values
• A new proof of the Hartman-Wintner law of the iterated logarithm
• On the last exit time and the number of exists of partial sums over a moving boundary
• Convergence rates for probabilities of moderate deviations for sums of random variables with multidimensional indices
• Marcinkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices
• Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law
• Exponential Convergence Rates for the Law of Large Numbers
• On the rate of Poisson convergence
• Stopped Random Walks
• Remainder term estimate for the asymptotic normality of the number of renewals
• On the coupon collector's remainder term
• ON Rényi's “Record” Problem and Engel's Series
• Convergence Rates in the Law of Large Numbers
• Convergence Rates for the Law of the Iterated Logarithm
• ON THE LAW OF THE ITERATED LOGARITHM
• Convergence Rates for Probabilities of Moderate Deviations
• An application of Fourier methods to the problem of sharpening the Berry-Esseen inequality