On Patterns in Sequences of Random Events |
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| Authors: | J. Gani A. Irle |
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| Affiliation: | (1) Australian National University, Canberra, Australia, AU;(2) University of Kiel, Germany, DE |
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| 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. Received 12 January 1998 in revised form 26 June 1998 |
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| Keywords: | 1991 Mathematics Subject Classification: 60J10 15A24 |
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