Related papers: Extrapolation Problem for Continuous Time Periodic…
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,…
We introduce stochastic sequences $\zeta(k)$ with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the…
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…
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…
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…
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…
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…
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…
We study stochastic sequences $\xi(k)$ with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the filtering…
We consider the problem of optimal estimation of the linear functional $A_N{\xi}=\sum_{k=0}^Na(k)\xi(k)$ depending on the unknown values of a stochastic sequence $\xi(m)$ with stationary increments from observations of the sequence…
We consider the problem of optimal linear estimation of the functional $$A_N \vec{\xi} =\sum_{j = 0}^{N} (\vec{a}(j))^{\top} \vec{\xi}(j)$$ that depends on the unknown values $\vec{\xi}(j),j=0,1,\dots,N,$ of a vector-valued harmonizable…
This paper is devoted to the error analysis of a time-spectral algorithm for fractional diffusion problems of order $\alpha$ ($0 < \alpha < 1$). The solution regularity in the Sobolev space is revisited, and new regularity results in the…
We study prediction in the functional linear model with functional outputs : $Y=SX+\epsilon $ where the covariates $X$ and $Y$ belong to some functional space and $S$ is a linear operator. We provide the asymptotic mean square prediction…
Misspecified models often provide useful information about the true data generating distribution. For example, if $y$ is a non-linear function of $x$ the least squares estimator $\hat{\beta}$ is an estimate of $\beta$, the slope of the best…
We consider a stochastic sequence $\xi(m)$ with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. The filtering…
It is increasingly common to encounter time-varying random fields on networks (metabolic networks, sensor arrays, distributed computing, etc.). This paper considers the problem of optimal, nonlinear prediction of these fields, showing from…
This paper discusses sparse isotropic regularization for a random field on the unit sphere $\mathbb{S}^2$ in $\mathbb{R}^{3}$, where the field is expanded in terms of a spherical harmonic basis. A key feature is that the norm used in the…
In functional linear regression, the slope ``parameter'' is a function. Therefore, in a nonparametric context, it is determined by an infinite number of unknowns. Its estimation involves solving an ill-posed problem and has points of…
The scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this…
Another way to evaluate the spectral-correlation properties of thermal fields of solids is suggested. Such a method takes into account detailed structure of the interface transition layer separating one bulk region from those of the vacuum…