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26 April 2024 |
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Spitzer's identity for discrete random walks | | A.J.E.M. Janssen
; Johan S.H. van Leeuwaarden
; | | Date: |
26 Oct 2017 | | 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 new derivation of Spitzer’s identity under the assumption
that the increments of the random walk have bounded jumps to the left. This
mild assumption facilitates a proof of Spitzer’s identity that only uses basic
properties of analytic functions and contour integration. The main novelty,
believed to be of broader interest, is a reversed approach that recognizes a
factored polynomial expression as the outcome of Cauchy’s formula. | | Source: | arXiv, 1710.9670 | | Services: | Forum | Review | PDF | Favorites | |
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