Spitzer's identity for discrete random walks

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

doi:10.1016/j.orl.2017.12.003

Spitzer's identity for discrete random walks

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

Center for Quantum Materials and Technology Eindhoven

Research output: Contribution to journal › Article › Academic › peer-review

1 Citation (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 language	English
Pages (from-to)	168-172
Number of pages	5
Journal	Operations Research Letters
Volume	46
Issue number	2
DOIs	https://doi.org/10.1016/j.orl.2017.12.003
Publication status	Published - 1 Mar 2018

Keywords

Complex analysis
Fluctuation theory
Spitzer's identity
Transform methods

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10.1016/j.orl.2017.12.003

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