On problems of predicting an isotropic random field on Hilbert space. (English. Russian original) Zbl 0834.60044

Kuznetsova, O. M.

Theory Probab. Math. Stat. 45, 59-65 (1992); translation from Teor. Veroyatn. Mat. Stat., Kiev 45, 62-69 (1991).

Summary: Solutions are obtained for the problem of predicting an isotropic random field on an infinite-dimensional Hilbert space from observations on a system of concentric spheres about the origin and from observations on a ball about the origin. Examples of a homogeneous and isotropic field and a Lévy field are considered.

MSC:

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

Keywords:

problem of predicting an isotropic random field; observations on a system of concentric spheres; Lévy field