Spitzer's identity for discrete random walks
| Autor: | Augustus J. E. M. Janssen, J.S.H. van Leeuwaarden |
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| Přispěvatelé: | Stochastic Operations Research, Center for Quantum Materials and Technology Eindhoven |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Fluctuation theory Applied Mathematics 010102 general mathematics Cauchy distribution Complex analysis Management Science and Operations Research 16. Peace & justice Random walk 01 natural sciences Methods of contour integration Industrial and Manufacturing Engineering Outcome (probability) Identity (music) 010104 statistics & probability Probability theory Bounded function Transform methods 0101 mathematics Software Analytic function Spitzer's identity |
| Zdroj: | Operations Research Letters, 46(2), 168-172. Elsevier |
| ISSN: | 0167-6377 |
| DOI: | 10.1016/j.orl.2017.12.003 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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