Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7543831 | Operations Research Letters | 2018 | 11 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
A.J.E.M. Janssen, J.S.H. van Leeuwaarden,