are independent random variables with zero mean and finite variance, xi ∈ [a, b] ⊂ R1, i = 1,..., n, form a random sample from a distribution with density % = 1/(b − a) (uniform distribution) and are independent of the errors ηi, i = 1,..., n. Unbiasedness and mean-square consistency of the examined estimators

It is shown that the uniform mean-square ergodic theorem holds for the family of wide sense stationary sequences, as soon as the random process with orthogonal increments, which corresponds to the orthogonal stochastic measure generated by means of the spectral representation theorem, is of bounded

Abstract. We study mean-square consistency, stability in the mean-square sense and meansquare convergence of drift-implicit linear multi-step methods with variable step-size for the approximation of the solution of Itô stochastic differential equations. We obtain conditions that depend on the step

We deal with linear multi-step methods for SDEs and study when the numerical approximation shares asymptotic properties in the mean-square sense of the exact solution. As in deterministic numerical analysis we use a linear time-invariant test equation and perform a linear stability analysis

This paper develops and explores applications of a linear shaping transformation that minimizes the mean squared error (MSE) between the original and shaped data, i.e., that results in an output vector with the desired covariance that is as close as possible to the input, in an MSE sense. Three

Absfracf-This paper presents a general approach to the deri-vation of series expansions of second-order wide-sense stationary mean-square continuous random process valid over an infinite-time interval. The coefficients of the expansion are orthogonal and con-vergence is in the mean-square sense

(t) is a Gaussian noise vector [1, 2]. To estimate s(t), we may use a beamformer with weights w so that s(t) = w*y(t), where s(t) is an estimate of s(t). To ensure that s(t) is close to s(t) in some sense, we may design the beamformer weights to minimize the MSE. However, since the MSE of a linear

in the mean-square sense under given conditions.

In this paper we consider the random initial value classical problem Ẋ(t) = f(X(t), t), t ∈ T = [t0, t1], X(t0) = X0. We give, based on the Euler numerical approach, new and weaker conditions on f for its convergence in the mean square sense. This work also presents the process to build

An approach to image modeling based on nonlinear mean-square estimation that does not assume a functio nal form for the model is described. The relationship between input and output images is represented in the form of a lookup table that can be efficiently computed from, and applied to images