Theory of Probability and Mathematical Statistics
On Lamperti transformation and AR(1) type characterisations of discrete random fields
Marko Voutilainen, Lauri Viitasaari and 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.
Keywords: Random fields, stationary fields, self-similar fields, Lamperti transformation, fractional Ornstein–Uhlenbeck fields
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