On a gateway between continuous and discrete Bessel and Laguerre processes
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Publication:2323058
DOI10.5802/AHL.13zbMATH Open1465.60073arXiv1807.09445OpenAlexW2964278931WikidataQ127791168 ScholiaQ127791168MaRDI QIDQ2323058
Author name not available (Why is that?)
Publication date: 30 August 2019
Published in: (Search for Journal in Brave)
Abstract: By providing instances of approximation of linear diffusions by birth-death processes, Feller [13], has offered an original path from the discrete world to the continuous one. In this paper, by identifying an intertwining relationship between squared Bessel processes and some linear birth-death processes, we show that this connection is in fact more intimate and goes in the two directions. As by-products, we identify some properties enjoyed by the birth-death family that are inherited from squared Bessel processes. For instance, these include a discrete self-similarity property and a discrete analogue of the beta-gamma algebra. We proceed by explaining that the same gateway identity also holds for the corresponding ergodic Laguerre semi-groups. It follows again that the continuous and discrete versions are more closely related than thought before, and this enables to pass information from one semi-group to the other one.
Full work available at URL: https://arxiv.org/abs/1807.09445
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