Miclo, Laurent and Patie, Pierre ORCID: 0000-0003-4221-0439
(2018)
On a gateway between continuous and discrete Bessel and Laguerre
processes.
Ann. H. Lebesgue, 2.
pp. 59-98.
Text
AHL_2019__2__59_0.pdf - Published Version Download (764kB) | Preview |
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.
Item Type: | Article |
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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: | 17 Mar 2024 07:52 |
DOI: | 10.5802/ahl.13 |
Related URLs: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3081726 |