Some results for skip-free random walk

  • Authors:

  • Mark Brown;Erol a. Peköz;Sheldon m. Ross

  • Affiliations:

  • Department of mathematics, city college, cuny, new york, ny e-mail: cybergarf@aol.com;School of management, boston university, boston, ma 02215, e-mail: pekoz@bu.edu;Department of industrial and system engineering, university of southern california, los angeles, ca 90089, e-mail: smross@usc.edu

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2010

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Abstract

A random walk that is skip-free to the left can only move down one level at a time but can skip up several levels. Such random walk features prominently in many places in applied probability including queuing theory and the theory of branching processes. This article exploits the special structure in this class of random walk to obtain a number of simplified derivations for results that are much more difficult in general cases. Although some of the results in this article have appeared elsewhere, our proof approach is different.