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Gambling Teams and Waiting Times for Patterns in Two-State Markov Chains

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Joseph Glaz ,
Martin Kulldorff ,
Vladimir Pozdnyakov  and
J. Michael Steele
Joseph Glaz*
Affiliation:
University of Connecticut
Martin Kulldorff*
Affiliation:
Harvard Medical School and Harvard Pilgrim Health Care
Vladimir Pozdnyakov*
Affiliation:
University of Connecticut
J. Michael Steele*
Affiliation:
University of Pennsylvania
*
∗ Postal address: Department of Statistics, University of Connecticut, 215 Glenbrook Road, U-4120, Storrs, CT 06269-4120, USA.
∗∗ Postal address: Department of Ambulatory Care and Prevention, Harvard Medical School, 133 Brookline Avenue, Boston, MA 02215-3920, USA.
∗ Postal address: Department of Statistics, University of Connecticut, 215 Glenbrook Road, U-4120, Storrs, CT 06269-4120, USA.
∗∗∗∗ Postal address: Department of Statistics, Wharton School, Huntsman Hall 447, University of Pennsylvania, Philadelphia, PA 19104, USA.
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Abstract

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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.

Keywords

Gamblingteamwaiting timepatternsuccess runfailure runMarkov chainmartingalestopping timegenerating function

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60G42: Martingales with discrete parameter
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 127 - 140
Copyright
© Applied Probability Trust 2006 

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