On a gateway between continuous and discrete Bessel and Laguerre processes

Miclo, Laurent and Patie, Pierre ORCID: 0000-0003-4221-0439
On a gateway between continuous and discrete Bessel and Laguerre processes. Annales Henri Lebesgue, 2019.

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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.

Item Type: Article
Additional Information: 47 pages
Uncontrolled Keywords: math.PR, math.PR, math.AP
Depositing User: Symplectic Admin
Date Deposited: 07 Apr 2020 10:54
Last Modified: 06 Jan 2022 08:29
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3081726