Summary
Let {X n} be a sequence of random variables assuming only values 0 and 1. A run of ones is a sequence of ones not interrupted by zeroes and preceded and followed by zeroes (except at the boundaries of the original sequence). The length of a run and the longest run within the first n observations are defined in the natural way.
Erdős and Révész (1975) (cf. also Samarova 1981; Guibas and Odlyzko 1980) gave a description of the almost sure asymptotic behaviour of the length of the longest run of ones from a coin-tossing sequence (i.e., the X nare i.i.d. r.v. with P(X n=0)=P(X n=1)=1/2). The present paper aims to extend their result to a certain class of stationary mixing sequences.
References
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Grill, K. Erdős-Révész type bounds for the length of the longest run from a stationary mixing sequence. Probab. Th. Rel. Fields 75, 77–85 (1987). https://doi.org/10.1007/BF00320082
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DOI: https://doi.org/10.1007/BF00320082
Keywords
- Stochastic Process
- Asymptotic Behaviour
- Probability Theory
- Statistical Theory
- Original Sequence