Simulation of normal distributed smooth fields by Karhunen-Loève expansion in combination with kriging (Q1128004)

Simulation of Gaussian smooth fields based on the Karhunen-Loéve expansion is considered. The problem of convergence of this expansion is discussed. The typical homogeneous isotropic covariance function has the form: \[ \text{Cov}(h)=2^{1-\nu}\Gamma^{-1}(\nu)(\alpha h^\beta)^\nu K_\nu(\alpha h^\beta),\quad h\geq 0, \] where \(K_\nu\) is the modified Bessel function of second kind of order \(\nu>0\) with parameters \(\alpha>0\) and \(0<\beta<2\).