An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law

DOI10.1051/ps:1998106zbMath0915.60049OpenAlexW2036516797MaRDI QIDQ4230642

Hartmut Lanzinger

Publication date: 7 February 1999

Published in: ESAIM: Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/104248

zbMATH Keywords

almost sure limit theoremincrements of partial sumsErdős-Rényi-Shepp law

Mathematics Subject Classification ID

Strong limit theorems (60F15)

Related Items

The strong law of large numbers for moving average of continuous state nonhomogeneous Markov chains, The generalized entropy ergodic theorem for nonhomogeneous bifurcating Markov chains indexed by a binary tree, Maxima of increments of partial sums for certain subexponential distributions, Functional Erdős-Rényi laws for semiexponential random variables

Cites Work

• The influence of extremes on the law of the iterated logarithm
• Riesz means and self-neglecting functions
• Limit laws of Erdős-Rényi-Shepp type
• Non-classical law of the iterated logarithm behaviour for trimmed sums
• Improved Erdoes-Renyi and strong approximation laws for increments of partial sums
• Limit theorems for delayed sums
• General Nörlund transforms and power series methods
• Erdös-Rényi-Shepp laws and weighted sums of independent identically distributed random variables
• On a problem of Csörgö and Révész
• On a family of summability methods and one-sided Tauberian conditions
• On a new law of large numbers
• Summability methods and almost sure convergence
• Tauberian theorems and large deviations
• Riesz and Valiron means and fractional moments
• ON ONE-SIDED TAUBERIAN CONDITIONS
• Limit theorems for moving averages of independent random vectors
• An approximation of partial sums of independent RV's, and the sample DF. II
• An approximation of partial sums of independent RV'-s, and the sample DF. I
• The strong law of large numbers when extreme terms are excluded from sums
• The approximation of partial sums of independent RV's
• Summability Methods for Independent, Identically Distributed Random Variables
• On a Necessary Condition for the Erdos-Renyi Law of Large Numbers
• Stability for sums of i.i.d. random variables when extreme terms are excluded
• Power series methods and almost sure convergence
• A Limit Law Concerning Moving Averages
• Large deviations of sums of independent random variables
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item