In this paper, we consider isotropic and stationary real Gaussian random fields defined on S2 × R and we investigate the asymptotic behavior, as +, of the empirical measure (excursion area) in S2 × [0] at any threshold, covering both cases when the field exhibits short and long memory, that is, integrable and nonintegrable temporal covariance. It turns out that the limiting distribution is not universal, depending both on the memory parameters and the threshold. In particular, in the long memory case a form of Berry s cancellation phenomenon occurs at zero-level, inducing phase transitions for both variance rates and limiting laws.

Marinucci, D., Rossi, M., Vidotto, A. (2021). Non-universal fluctuations of the empirical measure for isotropic stationary fields on S2×R. THE ANNALS OF APPLIED PROBABILITY, 31(5), 2311-2349 [10.1214/20-AAP1648].

Non-universal fluctuations of the empirical measure for isotropic stationary fields on S2×R

Rossi, Maurizia;
2021

Abstract

In this paper, we consider isotropic and stationary real Gaussian random fields defined on S2 × R and we investigate the asymptotic behavior, as +, of the empirical measure (excursion area) in S2 × [0] at any threshold, covering both cases when the field exhibits short and long memory, that is, integrable and nonintegrable temporal covariance. It turns out that the limiting distribution is not universal, depending both on the memory parameters and the threshold. In particular, in the long memory case a form of Berry s cancellation phenomenon occurs at zero-level, inducing phase transitions for both variance rates and limiting laws.
Articolo in rivista - Articolo scientifico
Spatio-temporal random fields; Berry's cancellation phenomenon; Central and NonCentral Limit Theorems; Wiener chaos.
English
29-ott-2021
2021
31
5
2311
2349
none
Marinucci, D., Rossi, M., Vidotto, A. (2021). Non-universal fluctuations of the empirical measure for isotropic stationary fields on S2×R. THE ANNALS OF APPLIED PROBABILITY, 31(5), 2311-2349 [10.1214/20-AAP1648].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/334798
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