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Simultaneous Occurrences of Runs in Independent Markov Chains

  • S. Robin
  • V. T. Stefanov
Article

Abstract

We observe m independent and identically distributed binary Markov chains and look for simultaneous occurrences of runs in several of them. We are interested in the distribution of the maximum number of simultaneous runs on finite time intervals. First we introduce a natural exact approach and also explain why it fails to calculate the required probabilities. Then we find exact upper and lower bounds for the probability of interest. We apply these results to detect genomic deletions in cancer patients.

Keywords

Comparative genomic hybridization Exact bounds Markov chains Simultaneous occurrences Runs 

AMS 2000 Subject Classification

Primary 60J05; Secondary 68R15 92D99 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.UMR 518 AgroParisTech/INRA Appl. Math. & Comput. Sci.ParisFrance
  2. 2.School of Mathematics and StatisticsThe University of Western AustraliaPerthAustralia

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