On occurrence of subpattern and method of gambling teams
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The expected value and generating function of the number of overlapping occurrences of a pattern P in a Markov chain until the first occurrence of a member from a finite collection of patterns that start with P is obtained. A martingale technique is employed to address the problem.
KeywordsPattern Gambling teams Waiting times Markov chains Martingales Test of randomness
Mathematics Subject Classification (2000)Primary 60C05 Primary 60G42 Secondary 60G40 Secondary 62E17
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