On sequential confidence estimation of parameters of stochastic dynamical systems with conditionally Gaussian noises

We consider the problem of non-asymptotical confidence estimation of linear parameters in multidimensional dynamical systems defined by general regression models with discrete time and conditionally Gaussian noises under the assumption that the number of unknown parameters does not exceed the dimension of the observed process. We develop a non-asymptotical sequential procedure for constructing a confidence region for the vector of unknown parameters with a given diameter and given confidence coefficient that uses a special rule for stopping the observations. A key role in the procedure is played by a novel property established for sequential least squares point estimates earlier proposed by the authors. With a numerical modeling example of a two-dimensional first order autoregression process with random parameters, we illustrate the possibilities for applying confidence estimates to construct adaptive predictions

Cumulative sum algorithms for automatic detection of gas well parameter changes

The problem of the change point detection in a sequence of random variables is considered. The task arises in control of technological processes, particularly, in oil and gas production management. Some equipment parameters are to be controlled in order to detect a change of the equipment characteristics and, consequently, a breakdown of its technological regime. As a rule, the data observed are stochastic with the unknown distribution

Estimating the efficiency of two algorithms for segmentation of digital radiation images of test objects

A mathematical model that describes digital radiation images of test objects is presented. Two algorithms are given for automatic segmentation of digital images distorted by additive noises. The efficiency of the algorithms is estimated based on mathematical modeling