Spitzer's identity for discrete random walks

A.J.E.M. Janssen, J. S.H. van Leeuwaarden

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)

Abstract

Spitzer's identity describes the position of a reflected random walk over time in terms of a bivariate transform. Among its many applications in probability theory are congestion levels in queues and random walkers in physics. We present a derivation of Spitzer's identity for random walks with bounded jumps to the left, only using basic properties of analytic functions and contour integration. The main novelty is a reversed approach that recognizes a factored polynomial expression as the outcome of Cauchy's formula.

Original languageEnglish
Pages (from-to)168-172
Number of pages5
JournalOperations Research Letters
Volume46
Issue number2
DOIs
Publication statusPublished - 1 Mar 2018

Funding

This work is supported by the NWO Gravitation Networks grant 024.002.003 and by ERC Starting Grant GA 259418 .

Keywords

  • Complex analysis
  • Fluctuation theory
  • Spitzer's identity
  • Transform methods

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