Modelling and Application of Stochastic Processes

1. Front Matter

   Pages i-xi

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2. Nested Orthogonal Realizations for Linear Prediction of Arma Processes

   • Jeffrey D. Klein, Bradley W. Dickinson

   Pages 1-23

3. q-Markov Covariance Equivalent Realizations

   • Robert E. Skelton, B. D. O. Anderson

   Pages 25-41

4. Reduced-Order Modelling of Stochastic Processes with Applications to Estimation

   • Uday B. Desai

   Pages 43-74

5. Generalized Principal Components Analysis and its Application in Approximate Stochastic Realization

   • K. S. Arun, S. Y. Kung

   Pages 75-104

6. Finite-Data Algorithms for Approximate Stochastic Realization

   • Richard J. Vaccaro

   Pages 105-122

7. Model Reduction via Balancing, and Connections with other Methods

   • Erik I. Verriest

   Pages 123-154

8. The Scattering Matrix Associated with a Stationary Stochastic Process: System Theoretic Properties and Role in Realization

   • Y. Avniel

   Pages 155-191

9. Realization and Reduction of S.I.S.O. Nonminimum Phase Stochastic Systems

   • Jitendra K. Tugnait

   Pages 193-214

10. On Stochastic Bilinear Systems

    • Arthur E. Frazho

    Pages 215-241

11. Markov Random Fields for Image Modelling & Analysis

    • Fernand S. Cohen

    Pages 243-272

12. Smoothing with Blackouts

    • Howard L. Weinert, Edward S. Chornoboy

    Pages 273-278

13. Stochastic Bilinear Models and Estimators with Nonlinear Observation Feedback

    • R. R. Mohler, W. J. Kolodziej

    Pages 279-288

The subject of modelling and application of stochastic 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 stochastic systems. Recently there has been considerable interest in the stochastic 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 stochastic realiza­ tion 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 ef­ ficient algorithms for obtaining reduced-order (approximate) stochastic 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).

• Estimator
• Phase
• Signal
• Stochastic processes
• Variance
• model
• modeling
• stochastic process

• Washington State University, Pullman, USA

  Uday B. Desai

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