Informatica

In this paper we give an introduction to collective risk theory in its simplest form. Our aims are to indicate how some basic facts may be obtained by martingale methods and to point out some open problems

Self-tuning control with recursive identification of extremal dynamic systems is considered. The systems can be represented by combinations of linear dynamic and extremal static parts, their output being disturbed by a coloured noise. Minimum-variance controllers for Hammerstein, Wiener, and Wiener-Hammerstein-type systems are designed taking into consideration restrictions for control signal magnitude and/or change rate. The estimates of unknown parameters in the controller equations are obtained in the identification process in the closed loop. The efficiency of self-tuning control algorithms is illustrated by statistical simulation. On the basis of worked out methods, adaptive systems for optimization of fuel combustion and steam condensation processes in thermal power units are developed.

A likelihood approach is considered to the problem of making inferences about the point t = ν in a Gaussian autoregressive sequence {Xt, t = 1 ÷ N} at which the underlying AR(p) parameters undergo a sudden change. The statistics of a loglikelihood function L(n, ν) is investigated over the admissible values n ∈ (p + 1, $\dots$ , N - 1) of a change point ν under validity of hypothesis of a change and no change. The expressions of L(n, ν) implying the loss of plausibility when moving away from the true change point ν are presented, and the probabilities P{$\bar{v}_{N}$ = ν± r}, r = 0,1,2, $\dots$, where $\bar{v}_{N}$ is the MLH estimate of a change point ν from the available realization x1,x2,…,xN of {Xt, t = 1 ÷ N} are considered.

The problem of determination of a change point in the properties of autoregressive sequences with unknown distribution is analysed. Two robust algorithms for the estimation of a change point when the distribution is symmetric and asymmetric are presented.

The problem multialternative recognition of non-stationary processes on the basis of dynamic models is investigated in the paper. The algorithms of pointwise and group classifications are compared. Clustering algorithms based on nonlinear mapping of the segments of random processes onto the plain are used to construct the classifiers.

The hierarchical principle of video-information analysis (progressive detalisation) is one from the set of principles which are implemented in the living vision system. The reflection of this principle in the techniques of the representation of a shape of the region, occupied by binary image, allows us to find a solution of two tasks simultaneously: data compression and data structure, which suits for geometric transformations of the image. This report includes operations which are performed on the hierarchical list of rectangles. The latter is built up by using intermediate pyramidal representation.

The problem of change point detection when the properties of the random process observed suddenly begin changing slowly is considered. The most probable time moments of changes are investigated. Random processes are described by autoregression equations. The situation is studied when slow changes in the properties of a random process take place according to the linear law. An example of solving the problem is presented, realized by computer.