Yu. V. Kozachenko

Boundary-Value problems with random initial conditions and functional series from subφ (Ω). I

We study conditions for convergence and the rate of convergence of random functional series from the space subφ (Ω) in various norms. The results are applied to the investigation of a boundary-value problem for a hyperbolic equation with random initial conditions.

On the uniform convergence of wavelet expansions of random processes from Orlicz spaces of random variables. II

We establish conditions under which there exists a function c(t) > 0 such that {fx1850-01}, where X(t) is a random process from an Orlicz space of random variables. We obtain estimates for the probabilities {fx1850-02}.

Distribution of the supremum of random processes from quasi-BanachK σ-spaces

We study random processes from quasi-BanachKσ-spaces of random variables whose domain of definition is not necessarily a compact set. We establish conditions under which the supremum of a properly normalized process belongs to the same space as the process itself. We also obtain estimates for the norm of this supremum.

Estimates of the supremum distribution for a certain class of random processes

Exponential estimates of the “tails” of supremum distributions are obtained for a certain class of pre-Gaussian random processes. The results obtained are applied to the quadratic forms of Gaussian processes and to processes representable as stochastic integrals of processes with independent increments.

Estimation of Parameters of Homogeneous Gaussian Random Fields

On the basis of the limit theorem for quadratic variation, we construct a consistent estimator for parameters of a homogeneous Gaussian random field of a certain class. We find confidence ellipsoids for estimators of this sort.

WORKS OF M. I. YADRENKO IN THE THEORY OF RANDOM FIELDS

A survey of the works of M. I. Yadrenko in the theory of random fields on finite-dimensional and infinite-dimensional spaces is presented.