A forecasting problem for homogeneous and isotropic random fields. (English. Russian original) Zbl 0835.60047

Sigal, B. M.

Theory Probab. Math. Stat. 47, 139-146 (1993); translation from Teor. Jmovirn. Mat. Stat. 47, 139-146 (1992).

Summary: A linear estimator is constructed for values of a homogeneous and isotropic random field in \({\mathbf R}^n\) given by its observations corrupted by additive “white noise” on a ball of finite radius. Optimal filters for the processes which are Fourier coefficients in the spectral expansion of the field are shown to satisfy second-order partial differential equations or an equivalent system of two first-order equations. By approximating the system with a finite-difference scheme, an efficient recursive procedure for solving the problem is worked out.

MSC:

60G60	Random fields
60G25	Prediction theory (aspects of stochastic processes)
62M20	Inference from stochastic processes and prediction

Keywords:

optimal filters; linear estimator; homogeneous and isotropic random field; partial differential equations