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HILBERT AND BANACH SPACE-VALUED STOCHASTIC PROCESSES
Buch von Yuichiro Kakihara
Sprache: Englisch

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Beschreibung
This is a development of the book entitled Multidimensional Second Order Stochastic Processes. It provides a research expository treatment of infinite-dimensional stationary and nonstationary stochastic processes or time series, based on Hilbert and Banach space-valued second order random variables. 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, Cramér and Karhunen classes as well as the stationary class. A new type of the Radon-Nikodým derivative of a Banach space-valued measure is introduced, together with Schauder basic measures, to study uniformly bounded linearly stationary processes.

Emphasis is on the use of functional analysis and 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. Generalizations are made to consider Banach space-valued stochastic processes to include processes of pth order for p ¿ 1. Readers may find that the covariance kernel is always emphasized and reveals another aspect of stochastic processes.

This book is intended not only for probabilists and statisticians, but also for functional analysts and communication engineers.
This is a development of the book entitled Multidimensional Second Order Stochastic Processes. It provides a research expository treatment of infinite-dimensional stationary and nonstationary stochastic processes or time series, based on Hilbert and Banach space-valued second order random variables. 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, Cramér and Karhunen classes as well as the stationary class. A new type of the Radon-Nikodým derivative of a Banach space-valued measure is introduced, together with Schauder basic measures, to study uniformly bounded linearly stationary processes.

Emphasis is on the use of functional analysis and 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. Generalizations are made to consider Banach space-valued stochastic processes to include processes of pth order for p ¿ 1. Readers may find that the covariance kernel is always emphasized and reveals another aspect of stochastic processes.

This book is intended not only for probabilists and statisticians, but also for functional analysts and communication engineers.
Details
Erscheinungsjahr: 2021
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: Gebunden
ISBN-13: 9789811211744
ISBN-10: 9811211744
Sprache: Englisch
Einband: Gebunden
Autor: Yuichiro Kakihara
Hersteller: World Scientific
Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße: 235 x 157 x 33 mm
Von/Mit: Yuichiro Kakihara
Erscheinungsdatum: 21.07.2021
Gewicht: 0,924 kg
Artikel-ID: 117420129
Details
Erscheinungsjahr: 2021
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: Gebunden
ISBN-13: 9789811211744
ISBN-10: 9811211744
Sprache: Englisch
Einband: Gebunden
Autor: Yuichiro Kakihara
Hersteller: World Scientific
Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße: 235 x 157 x 33 mm
Von/Mit: Yuichiro Kakihara
Erscheinungsdatum: 21.07.2021
Gewicht: 0,924 kg
Artikel-ID: 117420129
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