Gambling Teams and Waiting Times for Patterns in Two-State Markov Chains
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Gambling
teams
waiting times
patterns
success runs
failure runs
Markov chains
martingales
stopping times
generating functions
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Statistics and Probability
teams
waiting times
patterns
success runs
failure runs
Markov chains
martingales
stopping times
generating functions
Business
Statistics and Probability
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Abstract
Methods using gambling teams and martingales are developed and applied to find formulas for the expected value and the generating function of the waiting time until one observes an element of a finite collection of patterns in a sequence which is generated by a two-state first or higher order Markov chain.
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2006-03-01
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Journal of Applied Probability