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 |
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Pages (from-to) | 168-172 |
Number of pages | 5 |
Journal | Operations Research Letters |
Volume | 46 |
Issue number | 2 |
DOIs | |
Publication status | Published - 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