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Prof. Nikolai Leonenko

School of Mathematics, Cardiff University, UK

TITOLO: Limit theorems for the first Minkowski functional of Gaussian spatiotemporal random fields with long-memory

Abstract The paper [1] addresses the asymptotic analysis of sojourn functionals of spatiotemporal Gaussian random fields with long-range dependence (LRD) in time also known as long memory. Specifically, reduction theorems are derived for local functionals of nonlinear transformation of such fields, with Hermite rank m ? 1, under general covariance structures. These results are proven to hold, in particular, for a family of non?separable covariance structures belonging to Gneiting class. For m = 1, under some general condition on covariance structure of spatiotemporal random field with long memory in time, the properly normalized first Minkowski functional converge in distribution to the normal law. For m = 2, under separability of the spatiotemporal covariance function in space and time, the properly normalized Minkowski functional, involving the modulus of a Gaussian random field, converges in distribution to the Rosenblatt type limiting distribution for a suitable range of the long memory parameter. Some other related results can be found in [2,3]. For spatiotemporal isotropic stationary fields on sphere similar results obtained in Marinucci et al. [4] This is joint results with M.D.Ruiz-Medina (Granada University, Spain).

References [1] Leonenko, N.N. and Ruiz-Medina, M.D. (2023) Sojourn functionals for spatiotemporal Gaussian random fields with long-memory, Journal of Applied Probability, in press. [2] Leonenko N. and Olenko, A. (2014) Sojourn measures for Student and Fisher-Snedecor random fields, Bernoulli, 20 (3), 1454-1483 [3] Makogin, V. and Spodarev, E. (2022). Limit theorems for excursion sets of subordinated Gaussian random fields with long-range dependence, Stochastics, 94, 111?142 [4] Marinucci, D., Rossi, M. and Vidotto, A. (2020). Non-universal fluctuations of the empirical measure for isotropic stationary fields on S2 × R, Annals of Applied Probability, 31, 2311?2349

Il seminario si terrà il giorno 25 Gennaio 2023 ore 15:30 nella Aula C del Dipartimento Matematica e Applicazioni, Università di Napoli FEDERICO II, Complesso di Monte Sant'Angelo, Via Cintia, Napoli.

Link to Teams: https://teams.microsoft.com/l/meetup-join/19%3aMQ4RZDBo_0G-K_PHxKtktVYAczOGb...

Enrica Pirozzi

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