Advertisement

Probabilistic Recurrence Relations

  • M. Bhaskara Rao
  • S. Kasala
  • H. Zhang
Chapter

Abstract

A sampling of discrete probability problems, some of them coming from consulting work, is presented. We demonstrate how a probabilistic recurrence relation arises from the pit of the problem and present ways and means of solving the recurrence relation.

Keywords

Recurrence Relation Light Bulb Transition Probability Matrix Independent Copy Fibonacci Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

H. Zhang would like to thank the Department of Environmental Health at the University of Cincinnati for the support and splendid hospitality during his visits.

References

  1. 1.
    Balas B, Connor C (2004–2005) Look up and scream: Analytical difficulties in improv comedy. J Recreat Math 33:32–38Google Scholar
  2. 2.
    David F, Barton D (1962) Combinatorial chance. Hafner Publishing Company, New YorkGoogle Scholar
  3. 3.
    Durrett R (1996) Probability: Theory and examples, 2nd ed. Duxbury, BelmontGoogle Scholar
  4. 4.
    Durrett R (1999) Essentials of stochastic processes. Springer, New YorkMATHGoogle Scholar
  5. 5.
    Gerber H, Li S (1981) The occurrence of sequence patterns in repeated experiments and hitting times in Markov chains. Stoch Process Appl 11:101–108MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Li S (1980) A martingale approach to the study of occurence of sequence patterns in repeated experiments. Ann Prob 8:1171–1176 *Google Scholar
  7. 7.
    Pozdnyakov V, Kulldorff M (2006) Waiting times for patterns and a method of gambling teams. Am Math Mon 113:134–143MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Rao CR, Rao MB, Zhang H (2007) One bulb? Two bulbs? How many bulbs light up? A discrete probability problem involving dermal patches. Sankhyā 69:137–161MATHMathSciNetGoogle Scholar
  9. 9.
    Rao MB, Zhang H, Huang C, Chen F (2009) A discrete probability problem in bonding of molecules. PreprintGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of Environmental Health, Center for Genome InformationUniversity of CincinnatiCincinnatiUSA

Personalised recommendations