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On Patterns in Sequences of Random Events

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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.

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Authors and Affiliations

  1.  Australian National University, Canberra, Australia, , , , , , AU

    J. Gani

  2.  University of Kiel, Germany, , , , , , DE

    A. Irle

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  1. J. Gani
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  2. A. Irle
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Received 12 January 1998 in revised form 26 June 1998

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Gani, J., Irle, A. On Patterns in Sequences of Random Events. Mh Math 127, 295–309 (1999). https://doi.org/10.1007/s006050050041

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  • DOI: https://doi.org/10.1007/s006050050041

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