Construction and limit theorems for supCAR fields

Donhauzer, Illia, Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 and Olenko, Andriy 2026. Construction and limit theorems for supCAR fields. Journal of Theoretical Probability 39 (2) , 42. 10.1007/s10959-026-01499-0

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Abstract

The paper introduces a new class of random fields, supCAR fields, which are constructed as superpositions of continuous autoregressive random fields. These supCAR fields possess infinitely divisible marginal distributions. Their second-order properties are characterised by a novel family of covariance functions which can exhibit short- and long-range spatial dependencies. First, the existence of such fields is examined. Then, functional limit theorems for supCAR fields are derived under general assumptions. Four limiting scenarios that depend on the marginals of the underlying autoregressive fields and the specifications of the superposition are identified. Examples of specific supCAR fields, for which the assumptions and results are provided in simple, explicit forms, are presented. The obtained limit theorems can be employed for the statistical inference of supCAR fields.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Schools > Mathematics
Additional Information:	License information from Publisher: LICENSE 1: URL: http://creativecommons.org/licenses/by/4.0/, Type: open-access
Publisher:	Springer
ISSN:	0894-9840
Date of First Compliant Deposit:	15 April 2026
Date of Acceptance:	11 March 2026
Last Modified:	15 Apr 2026 09:01
URI:	https://orca.cardiff.ac.uk/id/eprint/186393

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