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The problem of optimal linear estimation of linear functionals depending on the unknown values of a periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the…

Statistics Theory · Mathematics 2025-10-29 Iryna Dubovets'ka , Mykhailo Moklyachuk

The problem of optimal linear estimation of a linear functional depending on the unknown values of periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the…

Statistics Theory · Mathematics 2025-11-20 Iryna Dubovets'ka , Mykhailo Moklyachuk

We propose solution of the problem of the mean square optimal estimation of linear functionals which depend on the unobserved values of a continuous time stochastic process with periodically correlated increments based on observations of…

Statistics Theory · Mathematics 2024-01-18 Maksym Luz , Mikhail Moklyachuk

We deal with the problem of optimal estimation of the linear functionals constructed from unobserved values of a continuous time stochastic process with periodically correlated increments based on past observations of this process. To solve…

Statistics Theory · Mathematics 2023-04-25 Maksym Luz , Mikhail Moklyachuk

The problem of mean square optimal estimation of linear functionals which depend on the unobserved values of a periodically correlated stochastic sequence is considered. The estimates are based on observations of the sequence with a noise.…

Statistics Theory · Mathematics 2020-02-12 Iryna Golichenko , Mikhail Moklyachuk

The problem of the mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional continuous time stationary stochastic process is considered. Estimates are based on observations of the…

Statistics Theory · Mathematics 2025-11-11 Oleksandr Masyutka , Mikhail Moklyachuk , Maria Sidei

This survey provides an overview of optimal estimation of linear functionals which depend on the unknown values of a stationary stochastic sequence. Based on observations of the sequence without noise as well as observations of the sequence…

Statistics Theory · Mathematics 2024-06-27 Mikhail Moklyachuk

The problem of optimal estimation of linear functionals constructed from the unobserved values of a stochastic sequence with periodically stationary increments based on observations of the sequence with stationary noise is considered. For…

Statistics Theory · Mathematics 2021-10-18 Maksym Luz , Mikhail Moklyachuk

We deal with the problem of the mean square optimal estimation of linear transformations of the unobserved values of a continuous time stochastic process with periodically correlated increments. Estimates are based on observations of the…

Statistics Theory · Mathematics 2024-02-12 Maksym Luz , Mikhail Moklyachuk

The problem of optimal estimation of linear functionals constructed from unobserved values of stochastic sequence with periodically stationary increments based on observations of the sequence with a periodically stationary noise is…

Statistics Theory · Mathematics 2025-11-10 Maksym Luz , Mykhailo Moklyachuk

The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a stochastic stationary sequence from observations of the sequence in special sets of points is considered. Formulas for…

Statistics Theory · Mathematics 2021-10-19 Oleksandr Masyutka , Mikhail Moklyachuk

The problem of the mean-square optimal linear estimation of functionals which depend on the unknown values of a stationary stochastic sequence from observations of the sequence with noise is considered. In the case of spectral certainty,…

Statistics Theory · Mathematics 2024-06-25 Maksym Luz , Mikhail Moklyachuk

The problem of optimal estimation of the linear functionals which depend on the unknown values of a periodically correlated stochastic sequence ${\zeta}(j)$ from observations of the sequence ${\zeta}(j)+{\theta}(j)$ at points…

Statistics Theory · Mathematics 2021-10-14 Iryna Golichenko , Oleksandr Masyutka , Mikhail Moklyachuk

The problem of mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional stationary stochastic sequence from observations of the sequence with a noise and missing observations is…

Statistics Theory · Mathematics 2024-02-13 Oleksandr Masyutka , Mikhail Moklyachuk , Maria Sidei

This paper focuses on the problem of the mean square optimal estimation of linear functionals which depend on the unknown values of a multidimensional stationary stochastic sequence. Estimates are based on observations of the sequence with…

Statistics Theory · Mathematics 2025-11-11 Oleksandr Masyutka , Mikhail Moklyachuk , Maria Sidei

We deal with the problem of optimal estimation of the linear functionals constructed from the missed values of a continuous time stochastic process $\xi(t)$ with periodically stationary increments at points $t\in[0;(N+1)T]$ based on…

Statistics Theory · Mathematics 2023-07-07 Maksym Luz , Mikhail Moklyachuk

The problem of optimal estimation of linear functional ${{A}_{N}}\xi =\sum\limits_{k=0}^{N}{a(k)\xi (k)}\,$ depending on the unknown values of a stochastic sequence $\xi (m)$ with stationary $n$-th increments from observations of the…

Statistics Theory · Mathematics 2025-10-28 Maksym Luz , Mykhailo Moklyachuk

The problem of the mean-square optimal linear estimation of the functional $A\xi=\ \int\limits_{R^s}a(t)\xi(-t)dt,$ which depends on the unknown values of stochastic stationary process $\xi(t)$ from observations of the process…

Statistics Theory · Mathematics 2025-10-21 Mykhailo Moklyachuk , Maria Sidei

The problem of the mean-square optimal linear estimation of the functional $A\xi=\ \int\limits_{R^s}a(t)\xi(-t)dt,$ which depends on the unknown values of stochastic stationary process $\xi(t)$ from observations of the process…

Statistics Theory · Mathematics 2024-02-13 Mikhail Moklyachuk , Maria Sidei

The problem of optimal linear estimation of functionals depending on the unknown values of a random field $\zeta(t,x)$, which is mean-square continuous periodically correlated with respect to time argument $t\in\mathbb R$ and isotropic on…

Statistics Theory · Mathematics 2024-02-13 Iryna Golichenko , Oleksandr Masyutka , Mikhail Moklyachuk
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