Functional Erdős-Rényi laws for semiexponential random variables

DOI10.1214/aop/1022855755zbMath0945.60026OpenAlexW2072846575MaRDI QIDQ1307489

Nina Gantert

Publication date: 24 September 2000

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

Full work available at URL: https://doi.org/10.1214/aop/1022855755

zbMATH Keywords

random walkslarge deviationsmoving averagessemi-exponential distributionsErdős-Rényi laws

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Large deviations (60F10) Functional limit theorems; invariance principles (60F17)

Related Items (13)

The maximum of a branching random walk with semiexponential increments ⋮ Non-central moderate deviations for compound fractional Poisson processes ⋮ Long strange segments, ruin probabilities and the effect of memory on moving average processes ⋮ Contraction principle for trajectories of random walks and Cramer's theorem for kernel-weighted sums ⋮ Sample path large deviations for Lévy processes and random walks with regularly varying increments ⋮ Large deviation results on some estimators for stationary Gaussian processes ⋮ Sample path large deviations for Lévy processes and random walks with Weibull increments ⋮ Large deviations for independent random variables – Application to Erdös-Renyi's functional law of large numbers ⋮ Large deviations of Poisson shot noise processes under heavy tail semi-exponential conditions ⋮ Characterization of a general class of tail probability distributions ⋮ Large deviations of means of heavy-tailed random variables with finite moments of all orders ⋮ The Large Deviation Principle for the On-Off Weibull Sojourn Process ⋮ Sample Path Large Deviations of Poisson Shot Noise with Heavy-Tailed Semiexponential Distributions

Cites Work

• Limit laws of Erdős-Rényi-Shepp type
• A functional limit theorem for Erdős and Rényi's law of large numbers
• On a new law of large numbers
• Large Deviations for Trajectories of Multi-Dimensional Random Walks
• An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law
• A Limit Law Concerning Moving Averages
• Boundary-Value Problems for Random Walks and Large Deviations in Function Spaces
• Large deviations for processes with independent increments
• An introduction to the theory of large deviations
• Large deviations of sums of independent random variables
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