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Books > Science & Mathematics > Physics > Classical mechanics > Sound, vibration & waves (acoustics)
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Modelling and Application of Stochastic Processes (Hardcover, 1986 ed.)
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Modelling and Application of Stochastic Processes (Hardcover, 1986 ed.)
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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)."
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