On a linear prediction problem for homogeneous random fields. (English. Russian original) Zbl 0835.60037

Moklyachuk, M. P.; Tatarinov, S. V.

Theory Probab. Math. Stat. 47, 119-127 (1993); translation from Teor. Jmovirn. Mat. Stat. 47, 118-129 (1992).

Summary: The problem considered is the optimal linear estimation of the transformation \[ {\mathbf A} \xi = \int^\infty_0 \int^\infty_0 a(t,s) \xi (t,s) dt ds \] of a homogeneous random field \(\xi (t,s)\) with spectral density \(f(\lambda, \mu)\) from observations of the field \(\xi (t,s)\) for \((t,s) \in {\mathbf R}^2 \backslash {\mathbf R}^2_+\). The least favorable spectral densities \(f^0 (\lambda, \mu) \in D\) and the minimax spectral characteristic of the optimal estimate of the transformation \({\mathbf A} \xi\) are found for various classes \(D\) of spectral densities.

MSC:

60G25	Prediction theory (aspects of stochastic processes)
93E11	Filtering in stochastic control theory
62M20	Inference from stochastic processes and prediction
93E10	Estimation and detection in stochastic control theory

Keywords:

optimal linear estimation; spectral characteristic; spectral densities