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

Marko Voutilainen; Lauri Viitasaari; Pauliina Ilmonen

doi:10.1090/tpms/1222

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

Marko Voutilainen, Lauri Viitasaari, Pauliina Ilmonen

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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.

Original language	English
Pages (from-to)	181-197
Journal	THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS
Volume	111
DOIs	https://doi.org/10.1090/tpms/1222
Publication status	Published - 2024
MoE publication type	A1 Journal article-refereed

Keywords

self-similar fields
Random fields
fractional Ornstein–Uhlenbeck fields
Lamperti transformation
stationary fields

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10.1090/tpms/1222

On Lamperti transformation and AR(1) type characterisations of discrete random fieldsAccepted author manuscript, 347 KBLicence: CC BY

Cite this

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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. ",

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AB - 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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KW - Random fields

KW - fractional Ornstein–Uhlenbeck fields

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

Abstract

Keywords

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FiRST Ilmonen: Finnish centre of excellence in Randomness and Structures

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

Abstract

Keywords

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FiRST Ilmonen: Finnish centre of excellence in Randomness and Structures

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