A1 Refereed original research article in a scientific journal
On Lamperti transformation and AR(1) type characterisations of discrete random fields
Authors: Voutilainen, Marko; Viitasaari, Lauri; Ilmonen, Pauliina
Publisher: American Mathematical Society
Publishing place: KYIV
Publication year: 2024
Journal:: Theory of Probability and Mathematical Statistics
Journal name in source: THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS
Journal acronym: THEOR PROBAB MATH ST
Volume: 111
First page : 181
Last page: 197
Number of pages: 17
ISSN: 0094-9000
eISSN: 1547-7363
DOI: https://doi.org/10.1090/tpms/1222
Web address : https://doi.org/10.1090/tpms/1222
Abstract
In this article we characterise discrete time stationary fields by difference equations involving stationary increment fields and self-similar fields. This gives connections between stationary fields, stationary increment fields and, through Lamperti transformation, self-similar fields. Our contribution is a natural generalisation of recently proved results covering the case of stationary processes.
In this article we characterise discrete time stationary fields by difference equations involving stationary increment fields and self-similar fields. This gives connections between stationary fields, stationary increment fields and, through Lamperti transformation, self-similar fields. Our contribution is a natural generalisation of recently proved results covering the case of stationary processes.
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