Modelling and Application of Stochastic Processes

by Uday B. Desai (Editor)

Overview

The subject of modelling and application of shastic processes is too vast to be exhausted in a single volume. In this book, attention is focused on a small subset of this vast subject. The primary emphasis is on realization and approximation of shastic systems. Recently there has been considerable interest in the shastic realization problem, and hence, an attempt has been made here to collect in one place some of the more recent approaches and algorithms for solving the shastic realization problem. Various different approaches for realizing linear minimum-phase systems, linear nonminimum-phase systems, and bilinear systems are presented. These approaches range from time-domain methods to spectral-domain methods. An overview of the chapter contents briefly describes these approaches. Also, in most of these chapters special attention is given to the problem of developing numerically efficient algorithms for obtaining reduced-order (approximate) shastic realizations. On the application side, chapters on use of Markov random fields for modelling and analyzing image signals, use of complementary models for the smoothing problem with missing data, and nonlinear estimation are included. Chapter 1 by Klein and Dickinson develops the nested orthogonal state space realization for ARMA processes. As suggested by the name, nested orthogonal realizations possess two key properties; (i) the state variables are orthogonal, and (ii) the system matrices for the (n + l)st order realization contain as their "upper" n-th order blocks the system matrices from the n-th order realization (nesting property).

Product Details

ISBN-13:	9780898381771
Publisher:	Springer US
Publication date:	10/31/1986
Edition description:	1986
Pages:	288
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

1. Nested Orthogonal Realizations for Linear Prediction of Arma Processes.- 2. q-Markov Covariance Equivalent Realizations.- 3. Reduced-Order Modelling of Shastic Processes with Applications to Estimation.- 4. Generalized Principal Components Analysis and its Application in Approximate Shastic Realization.- 5. Finite-Data Algorithms for Approximate Shastic Realization.- 6. Model Reduction Via Balancing, and Connections with Other Methods.- 7. The Scattering Matrix Associated with a Stationary Shastic Process: System Theoretic Properties and Role in Realization.- 8. Realization and Reduction of S.I.S.O. Nonminimum Phase Shastic Systems.- 9. On Shastic Bilinear Systems.- 10. Markov Random Fields for Image Modelling and Analysis.- 11. Smoothing with Blackouts.- 12. Shastic Bilinear Models and Estimators with Nonlinear Observation Feedback.