A strong invariance principle for the logarithmic average of sample maxima.

DOI10.1016/S0304-4149(00)00103-4zbMath1053.60030MaRDI QIDQ1888762

Ingo Fahrner

Publication date: 26 November 2004

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

zbMATH Keywords

Wiener processinvariance principlestrong approximationextremal processalmost sure behavior of extremes

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Extreme value theory; extremal stochastic processes (60G70) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17)

Related Items (6)

Strong approximation of maxima by extremal processes ⋮ On almost sure max-limit theorems of complete and incomplete samples from stationary sequences ⋮ Almost sure versions of the Darling-Erdős theorem ⋮ Almost sure convergence of sample range ⋮ Almost sure limit theorems for the maximum of stationary Gaussian sequences ⋮ Almost sure versions of distributional limit theorems for certain order statistics.

Cites Work

• On almost sure max-limit theorems
• Proof of the law of iterated logarithm through diffusion equation
• Extremes and related properties of random sequences and processes
• Invariance principle for the sum of minima
• An almost sure invariance principle for the partial sums of infima of independent random variables
• An extension of the almost sure max-limit theorem
• Embedding in extremal processes and the asymptotic behavior of sums of minima
• The logarithmic average of sample extremes is asymptotically normal.
• Almost sure convergence of sums of maxima and minima of positive random variables
• An approximation of partial sums of independent RV's, and the sample DF. II
• Almost Sure Convergence in Extreme Value Theory
• A Limit Theorem for Sums of Minima of Stochastic Variables
• Extremal Processes
• Asymptotic Normality of Sums of Minima of Random Variables
• The Rate of Growth of Sample Maxima
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