On the use of the Borel-Cantelli lemma in Markov chains

DOI10.1016/j.spl.2014.03.025zbMath1296.60084arXiv1110.2577OpenAlexW2034909660WikidataQ124880332 ScholiaQ124880332MaRDI QIDQ2453937

Alexei Stepanov

Publication date: 11 June 2014

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.2577

zbMATH Keywords

Markov chainsstrong limit lawsthe \(F^\alpha\)-schemethe Borel-Cantelli lemmathe concomitants of order statistics

Mathematics Subject Classification ID

Strong limit theorems (60F15) Limit theorems in probability theory (60F99)

Related Items (3)

Concomitants of records: limit results, generation techniques, correlation ⋮ A curious application of the Borel-Cantelli Lemmas, a result of Barndorff-Nielsen, and some open problems ⋮ Upper and lower bounds of Borel–Cantelli Lemma in a general measure space

Cites Work

• The Borel-Cantelli lemma
• Numbers of near bivariate record-concomitant observations
• Rate of convergence to the normal law of sums of induced order statistics
• Numbers of near-maxima for the bivariate case
• Convergence of sample paths of normalized sums of induced order statistics
• On the average difference between concomitants and order statistics
• Distribution of the maximum of concomitants of selected order statistics
• Bounds for probabilities of unions of events and the Borel-Cantelli lemma
• Wiener's test and Markov chains
• Extremal processes, secretary problems and the 1/e law
• Some remarks on nevzorov's record model
• The asymptotic theory of concomitants of order statistics
• On the distribution of the inter-record times in an increasing population
• Order Statistics
• Number of observations near the maximum in anF^α-scheme
• Bounds for the Probability of a Union, with Applications
• On the Rate of Growth of the Partial Maxima of a Sequence of Independent Identically Distributed Random Variables.
• On the Application of the Borel-Cantelli Lemma
• A generalization of the Borel-Cantelli lemma
• A note on the Borel-Cantelli lemma
• A note on the Borel-Cantelli lemma
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