The occurrence of sequence patterns in repeated experiments and hitting times in a Markov chain
A martingale argument is used to derive the generating function of the number of i.i.d. experiments it takes to observe a given string of outcomes for the first time. Then, a more general problem can be studied: How many trials does it take to observe a member of a finite set of strings for the first time? It is shown how the answer can be obtained within the framework of hitting times in a Markov chain. For these, a result of independent interest is derived.
Year of publication: |
1981
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Authors: | Gerber, Hans U. ; Li, Shuo-Yen Robert |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 11.1981, 1, p. 101-108
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Publisher: |
Elsevier |
Keywords: | Hitting times sequence patterns runs martingale |
Saved in:
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