Cargando…

Modelling and application of stochastic processes

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 consider...

Descripción completa

Detalles Bibliográficos
Autor principal: Desai, Uday
Lenguaje:eng
Publicado: Springer 1986
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-1-4613-2267-2
http://cds.cern.ch/record/2006400
_version_ 1780946309460525056
author Desai, Uday
author_facet Desai, Uday
author_sort Desai, Uday
collection CERN
description 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).
id cern-2006400
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 1986
publisher Springer
record_format invenio
spelling cern-20064002021-04-21T20:22:45Zdoi:10.1007/978-1-4613-2267-2http://cds.cern.ch/record/2006400engDesai, UdayModelling and application of stochastic processesMathematical Physics and Mathematics 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).Springeroai:cds.cern.ch:20064001986
spellingShingle Mathematical Physics and Mathematics
Desai, Uday
Modelling and application of stochastic processes
title Modelling and application of stochastic processes
title_full Modelling and application of stochastic processes
title_fullStr Modelling and application of stochastic processes
title_full_unstemmed Modelling and application of stochastic processes
title_short Modelling and application of stochastic processes
title_sort modelling and application of stochastic processes
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-1-4613-2267-2
http://cds.cern.ch/record/2006400
work_keys_str_mv AT desaiuday modellingandapplicationofstochasticprocesses