Search

Summary: In this paper the observation process of stochastic discrete‐time nonlinear system is analyzed. The system to be observed is assumed to be uncertain, but fulfilling the global "quasi‐Lipschitz" condition and is subjected to stochastic input and output disturbances of a white noise type. The combination of a traditional Luenberger residual term with a discontinuous one is considered. The designing of the best observer gain matrices is realized by using the Robust Attractive Ellipsoid Method for the analysis of the averaged observation error. The construction of this attractive ellipsoid is based on the numerical solution of some matrix optimization problem under specific constraints of Bilinear and Linear Matrix Inequalities (BMI's and LMI's) type applied to improve the attractiveness zone estimation. Two numerical xamples illustrate the effectiveness of the suggested approach. [ABSTRACT FROM AUTHOR]

We consider a problem of testing H0 : θ = θ0 against H1 : θ > θ0, where θ is a parameter of a discrete-time Markov process. We construct a locally most powerful sequential test, which maximizes the derivative of the power function at θ = θ0 in the class of level a sequential tests with the average sample size not greater than N. We construct a locally most powerful sequential test for an AR(1) autoregressive process with all unknown location parameter as an example. [ABSTRACT FROM AUTHOR]

Abstract: Let be a discrete-time stochastic process with a distribution , , where is an open subset of the real line. We consider the problem of testing a simple hypothesis : vs. a composite alternative : , where is some fixed point. The main goal of this article is to characterize the structure of locally most powerful sequential tests in this problem. For any sequential test with a (randomized) stopping rule and a (randomized) decision rule let be the type I error probability, the derivative, at , of the power function, and an average sample number of the test . Then we are concerned with the problem of maximizing in the class of all sequential tests such thatwhere and are some restrictions. It is supposed that is calculated under some fixed (not necessarily coinciding with one of ) distribution of the process . The structure of optimal sequential tests is characterized. [Copyright &y& Elsevier]

A general problem of testing two simple hypotheses about the distribution of a discrete-time stochastic process is considered. The main goal is to minimize an average sample number over all sequential tests whose error probabilities do not exceed some prescribed levels. As a criterion of minimization, the average sample number under a third hypothesis is used (modified Kiefer-Weiss problem). For a class of sequential testing problems, the structure of optimal sequential tests is characterized. An application to the Kiefer-Weiss problem for discrete-time stochastic processes is proposed. As another application, the structure of Bayes sequential tests for two composite hypotheses, with a fixed cost per observation, is given. The results are also applied for finding optimal sequential tests for discrete-time Markov processes. In a particular case of testing two simple hypotheses about a location parameter of an autoregressive process of order 1, it is shown that the sequential probability ratio test has the Wald-Wolfowitz optimality property. [ABSTRACT FROM AUTHOR]

Frequency analysis is often used to investigate the structure of systems representing multi-scale real-world phenomena. In many different environments, functional relationships characterized by a power law have been recognized, but, in many cases this simple model has turned out to be absolutely inadequate and other models have been proposed. In this paper, we propose a general abstract model which constitutes a unifying framework, including many models found in literature, like the mixed model, the exponential cut-off and the log-normal. It is based on a discrete-time stochastic process, which leads to a recurrence relation describing the temporal evolution of the system. The steady state solution of the system highlights the probability distribution, which underlies the frequency behavior. A particular instance of the general model, called cubic-cut-off, was analyzed and tested in a number of experiments, producing good answers in difficult cases, even in the presence of peculiar behaviors. [ABSTRACT FROM AUTHOR]