2019
Том 71
№ 9

# Moklyachuk M. P.

Articles: 6
Article (Ukrainian)

### Robust interpolation of random fields homogeneous in time and isotropic on a sphere, which are observed with noise

Ukr. Mat. Zh. - 1995. - 47, № 7. - pp. 962–970

We study the problem of optimal linear estimation of the functional $$A_N \xi = \sum\limits_{k = 0}^{\rm N} {\int\limits_{S_n } {a(k,x)\xi (k,x)m_n (dx),} }$$ , which depends on unknown values of a random field ξ(k, x),k∃Z,x∃S n homogeneous in time and isotropic on a sphereS n, by observations of the field ξ(k,x)+η(k,x) with k∃ Z{0, 1, ...,N},x∃Sn (here, η (k, x) is a random field uncorrelated with ξ(k, x), homogeneous in time, and isotropic on a sphere Sn). We obtain formulas for calculation of the mean square error and spectral characteristic of the optimal estimate of the functionalA Nξ. The least favorable spectral densities and minimax (robust) spectral characteristics are found for optimal estimates of the functionalA Nξ.

Article (Russian)

### On minimax filtration of vector processes

Ukr. Mat. Zh. - 1993. - 45, № 3. - pp. 389–397

We study the problem of optimal linear estimation of the transformation $A\xi = \smallint _0^\infty< a(t), \xi ( - t) > dt$ of a stationary random process $ξ(t)$ with values in a Hilbert space by observations of the process $ξ(t) + η(t)$ for $t ⩽ 0$. We obtain relations for computing the error and the spectral characteristic of the optimal linear estimate of the transformation $Aξ$ for given spectral densities of the processes $ξ(t)$ and $η(t)$. The minimax spectral characteristics and the least favorable spectral densities are obtained for various classes of densities.

Article (Ukrainian)

### Extrapolation of transformations of random processes perturbed by white noise

Ukr. Mat. Zh. - 1991. - 43, № 2. - pp. 216–223

Article (Ukrainian)

### Minimax filtration of linear transformations of stationary sequences

Ukr. Mat. Zh. - 1991. - 43, № 1. - pp. 92-99

Article (Ukrainian)

### A filtration of transformations of random sequences

Ukr. Mat. Zh. - 1985. - 37, № 6. - pp. 730–734

Article (Ukrainian)

### Linear interpolation of a homogeneous random vector field of a continuous argument

Ukr. Mat. Zh. - 1977. - 29, № 3. - pp. 324–332