CS07: Stochastic Properties of Time-Dependent Random Fields

Organizer: Anna Vidotto (University of Naples Federico II)

Limit theorems for spatiotemporal functionals of Gaussian fields

Leonardo Maini (Università di Roma Tor Vergata)

Our study focuses on limit theorems for spatiotemporal functionals of Gaussian fields, with a particular emphasis on the differences between the separable case, where the covariance structure is a tensor product of the spatial and temporal covariances, and the Gneiting class. Specifically, we highlight the assumptions required to derive a central or non-central limit theorem for these functionals. This work is based on a recent publication and ongoing research with N. Leonenko, I. Nourdin and F. Pistolato.

Statistical inference for cylindrical processes on the sphere

Radomyra Shevchenko (Université Côte d’Azur / Centrale Méditerranée)

In this talk, I will present a parameter estimation method for time-dependent random fields on the unit sphere, with a particular focus on the spherical fractional Brownian motion defined as a cylindrical process with respect to the spherical harmonics. I will introduce a Hurst parameter estimator based on quadratic variations computed along a single geodesic line in space, using observations at two time points, and discuss its asymptotic properties.