Table of Contents
Journal of Probability
Volume 2014, Article ID 646140, 6 pages
Research Article

On the Expected Number of Limited Length Binary Strings Derived by Certain Urn Models

1Department of Mathematics, University of Patras, 26500 Patras, Greece
2Department of Physics, University of Patras, 26500 Patras, Greece

Received 27 July 2014; Accepted 7 October 2014; Published 27 October 2014

Academic Editor: Tae-Sung Kim

Copyright © 2014 Frosso S. Makri and Zaharias M. Psillakis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The expected number of 0-1 strings of a limited length is a potentially useful index of the behavior of stochastic processes describing the occurrence of critical events (e.g., records, extremes, and exceedances). Such model sequences might be derived by a Hoppe-Polya or a Polya-Eggenberger urn model interpreting the drawings of white balls as occurrences of critical events. Numerical results, concerning average numbers of constrained length interruptions of records as well as how on the average subsequent exceedances are separated, demonstrate further certain urn models.