On Lamperti transformation and AR(1) type characterisations of discrete random fields



: Voutilainen, Marko; Viitasaari, Lauri; Ilmonen, Pauliina

Publisher: American Mathematical Society

: KYIV

: 2024

: Theory of Probability and Mathematical Statistics

: THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS

: THEOR PROBAB MATH ST

: 111

: 181

: 197

: 17

: 0094-9000

: 1547-7363

DOI: https://doi.org/10.1090/tpms/1222

: https://doi.org/10.1090/tpms/1222


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.



Last updated on 2025-27-01 at 19:15