Longest runs in a sequence of \(m\)-dependent random variables

DOI10.1007/BF01192057zbMath0739.60043MaRDI QIDQ1182493

Serguei Novak

Publication date: 28 June 1992

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

rate of convergencelongest head runBernoulli independent trials

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Extreme value theory; extremal stochastic processes (60G70) Sums of independent random variables; random walks (60G50)

Related Items (13)

Binomial approximation for sum of indicators with dependent neighborhoods ⋮ On the length of the longest head run ⋮ The Hausdorff dimension of level sets described by Erdős-Rényi average ⋮ Some results associated with the longest run in a strongly ergodic Markov chain ⋮ Long strange segments, ruin probabilities and the effect of memory on moving average processes ⋮ 1-dependent stationary sequences for some given joint distributions of two consecutive random variables ⋮ On the length of the longest run in a multi-state Markov chain. ⋮ Runs in continuous-valued sequences ⋮ On the strong law of large numbers for sums over increasing runs ⋮ A note on runs of geometrically distributed random variables ⋮ On the asymptotics of the number of binary words with a given length of a maximal series ⋮ On the length of the longest increasing run in \(\mathbb{R}^d\) ⋮ Strong laws for the maximal gain over increasing runs

Cites Work

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• The Erdős-Rényi law in distribution, for coin tossing and sequence matching
• Three problems on the lengths of increasing runs
• An extreme value theory for long head runs
• Erdős-Révész type bounds for the length of the longest run from a stationary mixing sequence
• Time intervals of constant sojourn of a homogeneous Markov chain in a fixed subset of states
• Two moments suffice for Poisson approximations: The Chen-Stein method
• Limiting behavior of a process of runs
• On a new law of large numbers
• Long repetitive patterns in random sequences
• Success runs in a two-state Markov chain
• On the field of combinatory analysis

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