Gambling Teams and Waiting Times for Patterns in Two-State Markov Chains
Joseph Glaz, Martin Kulldorff, V. A. Pozdnyakov, John M. Steele · Journal of Applied Probability · 2006
Methods using gambling teams and martingales are developed and applied to find formulae for the expected value and the generating function of the waiting time to observation of an element of a finite collection of patterns in a sequence generated by a two-state Markov chain of first, or higher, order.