Regularity and convergence analysis in Sobolev and Hölder spaces for generalized Whittle–Matérn fields
Regularity and convergence analysis in Sobolev and Hölder spaces for generalized Whittle–Matérn fields
We analyze several Galerkin approximations of a Gaussian random field $\mathcal{Z}\colon\mathcal{D}\times\Omega\to\mathbb{R}$ indexed by a Euclidean domain $\mathcal{D}\subset\mathbb{R}^d$ whose covariance structure is determined by a negative fractional power $L^{-2\beta}$ of a second-order elliptic differential operator $L:= -\nabla\cdot(A\nabla) + \kappa^2$. Under minimal assumptions on the domain $\mathcal{D}$, the coefficients $A\colon\mathcal{D}\to\mathbb{R}^{d\times d}$, $\kappa\colon\mathcal{D}\to\mathbb{R}$, …