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 | |
| Publication status | Published - 1 Mar 2018 |
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Keywords
- Complex analysis
- Fluctuation theory
- Spitzer's identity
- Transform methods
Cite this
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Spitzer's identity for discrete random walks. / Janssen, A.J.E.M.; van Leeuwaarden, J. S.H.
In: Operations Research Letters, Vol. 46, No. 2, 01.03.2018, p. 168-172.Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - Spitzer's identity for discrete random walks
AU - Janssen, A.J.E.M.
AU - van Leeuwaarden, J. S.H.
PY - 2018/3/1
Y1 - 2018/3/1
N2 - 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.
AB - 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.
KW - Complex analysis
KW - Fluctuation theory
KW - Spitzer's identity
KW - Transform methods
UR - http://www.scopus.com/inward/record.url?scp=85040306793&partnerID=8YFLogxK
U2 - 10.1016/j.orl.2017.12.003
DO - 10.1016/j.orl.2017.12.003
M3 - Article
AN - SCOPUS:85040306793
VL - 46
SP - 168
EP - 172
JO - Operations Research Letters
JF - Operations Research Letters
SN - 0167-6377
IS - 2
ER -