Quadratic variations method for parameter estimation

A popular modeling ansatz for turbulent processes in Geophysics, but also for other "chaotic" quantities in Geosciences and Cosmology, are random fields, and the spectrum of such quantities can be an important characteristic in applications. However, missing or irregular observations can easily lead to imprecisions in the spectral domain. In this talk, we show how the quadratic variations method can be used to define simple estimators for parameters intrinsically related to the spectrum, and also provide some estimation ideas for space-time random fields.
We focus on isotropic Gaussian random fields on the unit sphere and the Matérn process on the plane. If time allows, we will also talk about parameter estimation from space-time observations of the solution of the fractional-white wave equation.