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On Patterns in Sequences of Random Events (1999)

Gani, J. ; Irle, A.

Springer

Monatshefte für Mathematik 127 (1999), S. 295-309

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ISSN: 1436-5081

Keywords: 1991 Mathematics Subject Classification: 60J10 ; 15A24 ; Key words: Sequences of events ; independent trials ; Markovian trials ; repetitions ; avoidance of a pattern ; Markov chain

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract. This paper considers patterns of particular events 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s006050050041

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