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

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

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.