Multidimensional second order stochastic processes

by Kakihara, Yuichiro

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Title Statements

Full title :Multidimensional second order stochastic processes

Summary

This book provides a research-expository treatment of infinite-dimensional nonstationary stochastic processes or times series. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, "V"--Bounded, Cramer and Karhunen classes and also the stationary class. Emphasis is on the use of functional, harmonic analysis as well as probability theory. Applications are made from the probabilistic and statistical points of view to prediction problems, Kalman filter, sampling theorems and strong laws of large numbers. Readers may find that the covariance kernel analysis is emphasized and it reveals another aspect of stochastic processes. This book is intended not only for probabilists and statisticians, but also for communication engineers.

A research-expository treatment of infinite-dimensional nonstationary stochastic processes (or time series) on a locally compact abelian group is provided with this book. Stochastic measures and scalar or operator bimeasures are fully discussed.

Edition Statements

Publication Date:1997

Publication Statements

Publisher(s):World Scientific Publishing
Place of Publication:Singapore
Language:eng
Publication Date:1997

The Physical Object

Description:331 s

Edition Identifiers

ISBN:9810230001, 9789810230005
oclc:ocn476700790
LC Classification:QA274
Dewey Decimal:519.2

Introduction and preliminaries; Hilbert modules and covariance kernels; stochastic measures and operator-valued bimeasures; multidimensional stochastic processes; special topics; applications.