Dear all,

we are pleased to announce the following seminar at the Department of Statistical Sciences, Sapienza University.

——— *Speaker*: Nikolai Leonenko, Cardiff University (UK) *Title*: *Limit theorems for supCAR random fields*

*When*: Monday, September 22, 10:00 *Where*: p.le A. Moro, 5, building CU002, room 24 (fourth floor) *Online: *at the following link https://meet.google.com/fhc-xvdh-cgq

*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.

These are joint results with Illia Donhauzer https://arxiv.org/search/math?searchtype=author&query=Donhauzer,+I (Kyushu University, Japan) and Andriy Olenko https://arxiv.org/search/math?searchtype=author&query=Olenko,+A (La Trobe University, Melbourne, Australia) ———

Best regards, Luisa Beghin

*************************************************************** Luisa Beghin Dipartimento di Scienze Statistiche Fac. Ingegneria dell'Informazione, Informatica e Statistica "SAPIENZA" Università di Roma Piazzale Aldo Moro 5, 00185 Roma T (+39) 06 49910709 https://sites.google.com/site/luisabeghin/ *****************************************************************