Minimax filtering of time-homogeneous isotropic random fields on a sphere. (English. Ukrainian original) Zbl 0861.60060

Moklyachuk, M. P.

Theory Probab. Math. Stat. 49, 137-146 (1994); translation from Teor. Jmovirn. Mat. Stat. 49, 193-205 (1993).

Summary: The problem of the least mean-square linear estimation of the transformation \[ A\xi=\int^\infty_0 \int_{S_n} a(t,x)\xi(-t,x)m_n(dx)dt \] of a time-homogeneous isotropic on a sphere \(S_n\) random field \(\xi(t,x)\) from observations of the field \(\xi(t,x)+\eta(t,x)\) for \(t\leq 0\), \(x\in S_n\), where \(\eta(t,x)\) is a time-homogeneous isotropic on a sphere \(S_n\) random field uncorrelated with \(\xi(t,x)\), is considered. The least favorable spectral densities and the minimax (robust) spectral characteristics of the optimal estimates of the transformation \(A\xi\) are determined for some classes of spectral densities.

MSC:

60G60	Random fields
60G35	Signal detection and filtering (aspects of stochastic processes)
62M20	Inference from stochastic processes and prediction
93E11	Filtering in stochastic control theory

Keywords:

least mean-square linear estimation; time-homogeneous isotropic on a sphere; spectral characteristics; optimal estimates; spectral densities