On patterns in sequences of random events

J. Gani; A. Irle

doi:10.1007/s006050050041

On patterns in sequences of random events

J. Gani^*, A. Irle

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

This paper considers patterns of particular events A₁,...,A_k(k ≥ 2) in sequences of trials, some independent and others Markovian. Matrix recursions are found for the number of sequences of length n avoiding a specific pattern, and the associated probability of this event is evaluated. A Markov chain method for the study of such problems is outlined, and is illustrated in various cases. Finally, configurations of length 3 in Bernoulli trials are examined as an example.

Original language	English
Pages (from-to)	295-309
Number of pages	15
Journal	Monatshefte fur Mathematik
Volume	127
Issue number	4
DOIs	https://doi.org/10.1007/s006050050041
Publication status	Published - 1999

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10.1007/s006050050041

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title = "On patterns in sequences of random events",

abstract = "This paper considers patterns of particular events A1,...,Ak(k ≥ 2) in sequences of trials, some independent and others Markovian. Matrix recursions are found for the number of sequences of length n avoiding a specific pattern, and the associated probability of this event is evaluated. A Markov chain method for the study of such problems is outlined, and is illustrated in various cases. Finally, configurations of length 3 in Bernoulli trials are examined as an example.",

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AB - This paper considers patterns of particular events A1,...,Ak(k ≥ 2) in sequences of trials, some independent and others Markovian. Matrix recursions are found for the number of sequences of length n avoiding a specific pattern, and the associated probability of this event is evaluated. A Markov chain method for the study of such problems is outlined, and is illustrated in various cases. Finally, configurations of length 3 in Bernoulli trials are examined as an example.

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KW - Markovian trials

KW - Repetitions

KW - Sequences of events

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JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

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On patterns in sequences of random events

Abstract

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