Thesis (Ph. D.)--University of Washington, 1986. / Vita. Bibliography: leaves [81]-83.

Thesis (M.S. in electrical engineering)--Washington State University, May 2007. / Includes bibliographical references (p. 17-18).

Decoupling control is widely applied to multi-input multi-output industrial processes. The traditional decoupling control methods are based on accurate models, however it is difficult or impossible to obtain accurate models in practice. Moreover, the traditional decoupling control methods are not suitable for the analysis of the couplings among system outputs which are subjected to the random noises. To solve the problems mentioned above, we will look into the decoupling control problem in probability sense. To describe this control problem, probabilistic decoupling has been presented as a novel concept based on statistical independence. Using probability theory, a set of new control objectives has been extended by this presented concept. Conditions of probabilistic complete decoupling are given. Meanwhile, the relationship between the traditional decoupling and probabilistic decoupling has been analyzed in this thesis, theoretically. To achieve the control objectives of probabilistic decoupling, various control algorithms are developed for dynamic multi-variable stochastic systems, which are represented by linear stochastic models, bilinear stochastic models and stochastic nonlinear models, respectively. For linear stochastic models subjected to Gaussian noises, the covariance control theory has been used. The Output-feedback stabilization via block backstepping design has been considered for bilinear stochastic systems subjected to Gaussian noises. Furthermore, the minimum mutual information control has been proposed for stochastic nonlinear systems subjected to non-Gaussian noises. Some advanced topics are also considered in this thesis. The stochastic feedback linearization can be applied to a class of stochastic nonlinear systems and the reduced-order closed-form covariance control models are also presented, which can be applied in covariance control theory. Using kernel density estimation, data-based minimum mutual information control is given to extend the presented minimum mutual information control algorithm.

Cordeiro & Ferrari (1991) use the asymptotic expansion of Harris (1985) for the moment generating function of the score statistic to produce a generalization of Bartlett adjustment for application to the score statistic. It is shown here that Harris's expansion is not invariant under reparameterization and an invariant expansion is derived using a method based on the expected likelihood yoke. A necessary and sufficient condition for the existence of a generalized Bartlett adjustment for an arbitrary statistic is given in terms of its moment generating function. Generalized Bartlett adjustments to the likelihood ratio and score test statistics are derived in the case where the interest parameter is one-dimensional under the assumption of a mis-specified model, where the true distribution is not assumed to be that under the null hypothesis.

Over recent years, we have witnessed a rapid development in the body of economic theory with applications to finance. It has had great success in finding theoretical explanations to economic phenomena. Typically, theories are employed that are defined by mathematical models. Finance in particular has drawn upon and developed the theory of stochastic differential equations. These produce elegant and tractable frameworks which help us to better understand the world. To directly apply such theories, the models must be assessed and their parameters estimated. Implementation requires the estimation of the model's elements using statistical techniques. These fit the model to the observed data. Unfortunately, existing statistical methods do not work satisfactorily when applied to many financial models. These methods, when applied to complex models often yield inaccurate results. Consequently, simpler analytical models are often preferred, but these are typically unrealistic representations of the underlying process, given the stylised facts reported in the literature. In practical applications, data is observed at discrete intervals and a discretisation is typically used to approximate the continuous-time model. This can lead to biased estimates, since the true underlying model is assumed continuous. This thesis develops new methods to estimate these types of models, with the objective of obtaining more accurate estimates of the underlying parameters present. The methods are applicable to general models. As the solution to the true continuous process is rarely known for these applications, the methods developed rely on building an Euler-Maruyama approximate model and using simulation techniques to obtain the distribution of the unknown quantities of interest. We propose to simulate the missing paths between the observed data points to reduce the bias from the approximate model. Alternatively, one could use a more sophisticated scheme to discretise the process. Unfortunately, their implementation with simulation methods require us to simulate from the density and evaluate the density at any given point. This has until now only been possible for the Euler-Maruyama scheme. One contribution of the thesis is to show the existence of a closed form solution from use of the higher order Milstein scheme. The likelihood based method is implemented within the Bayesian paradigm, as in the context of these models, Bayesian methods are often analytically easier. Concerning the estimation methodology, emphasis is placed on simulation efficiency; design and implementation of the method directly affects the accuracy and stability of the results. In conjunction with estimation, it is important to provide inference and diagnostic procedures. Meaningful information from simulation results must be extracted and summarised. This necessitates developing techniques to evaluate the plausibility and hence the fit of a particular model for a given dataset. An important aspect of model evaluation concerns the ability to compare model fit across a range of possible alternatives. The advantage with the Bayesian framework is that it allows comparison across non-nested models. The aim of the thesis is thus to provide an efficient estimation method for these continuous-time models, that can be used to conduct meaningful inference, with their performance being assessed through the use of diagnostic tools.

University of Macau / Faculty of Science and Technology / Department of Mathematics

M.Sc (Computer Science.) / This dissertation details the implementation of SNAP, a stochastic network analysis package, as the basis of an in-house computer configuration planning facility. The work was performed at Head Office, Gold Fields of South Africa Limited, Johannesburg, South Africa (GFSA) during the period April 1980 to December 1981. SNAP was developed by the Institute of Applied Computer Science at the University of Stellenbosch, Stellenbosch, South Africa. The implementation of SNAP at GFSA signalled the first in-house SNAP facility, and the first SNAP implementation on an ICL computer (although implementation had been in progress at another ICL site since 1979). Although this dissertation is very specific in nature, it is intended to provide an insight into the methodology employed in planning and implementing an in-house configuration planning facility. An overview of multiclass queueing network models and the SNAP package is provided, although no attempt is made to explain the stochastic theory of queueing networks in any detail. Attention is thereafter focussed on the various phases of the project. Problems were encountered in monitoring performance data, and these are looked at in some depth. The question of workload characterization and the difficulties of producing a satisfactory GFSA classification strategy are then presented. The model design, calibration and validation stages are explained using the GFSA model. Thereafter, use of the model for prediction purposes is illustrated by means of a number of examples. Finally, tne memory management model is discussed - main memory does not form part of the SNAP model and has to be dealt with as a separate issue.

No description available.

Please read the abstract/summary in the section 00back of this document. / Thesis (PhD (Applied Mathematics))--University of Pretoria, 2006. / Mathematics and Applied Mathematics / unrestricted

In this thesis we consider estimation of the tail index for heavy tailed stochastic volatility models with long memory. We prove a central limit theorem for a Hill estimator. In particular, it is shown that neither the rate of convergence nor the asymptotic variance is affected by long memory. The theoretical findings are verified by simulation studies.