Hilbert and Banach space-valued stochastic processes:
"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 vari...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
©2021
|
| Schriftenreihe: | Series on multivariate analysis
vol. 13 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "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."-- |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | 1 Online-Ressource (540 Seiten) |
| ISBN: | 9789811211751 9811211752 |
| DOI: | 10.1142/11592 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| doi_str_mv | 10.1142/11592 |
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| id | DE-604.BV047457860 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:05:17Z |
| indexdate | 2024-07-10T09:12:41Z |
| institution | BVB |
| isbn | 9789811211751 9811211752 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032859695 |
| oclc_num | 1268192710 |
| open_access_boolean | |
| physical | 1 Online-Ressource (540 Seiten) |
| psigel | ZDB-124-WOP |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | World Scientific |
| record_format | marc |
| series2 | Series on multivariate analysis |
| spelling | Kakihara, Yūichirō Verfasser aut Hilbert and Banach space-valued stochastic processes Yûichirô Kakihara Singapore World Scientific ©2021 1 Online-Ressource (540 Seiten) txt rdacontent c rdamedia cr rdacarrier Series on multivariate analysis vol. 13 Includes bibliographical references and index "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."-- Stochastic processes Hilbert space Banach spaces Radon-Nikodym property Functional analysis Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Electronic books Stochastischer Prozess (DE-588)4057630-9 s DE-604 Erscheint auch als Druck-Ausgabe 9789811211744 Erscheint auch als Druck-Ausgabe 9811211744 https://doi.org/10.1142/11592 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Kakihara, Yūichirō Hilbert and Banach space-valued stochastic processes Stochastic processes Hilbert space Banach spaces Radon-Nikodym property Functional analysis Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 |
| title | Hilbert and Banach space-valued stochastic processes |
| title_auth | Hilbert and Banach space-valued stochastic processes |
| title_exact_search | Hilbert and Banach space-valued stochastic processes |
| title_exact_search_txtP | Hilbert and Banach space-valued stochastic processes |
| title_full | Hilbert and Banach space-valued stochastic processes Yûichirô Kakihara |
| title_fullStr | Hilbert and Banach space-valued stochastic processes Yûichirô Kakihara |
| title_full_unstemmed | Hilbert and Banach space-valued stochastic processes Yûichirô Kakihara |
| title_short | Hilbert and Banach space-valued stochastic processes |
| title_sort | hilbert and banach space valued stochastic processes |
| topic | Stochastic processes Hilbert space Banach spaces Radon-Nikodym property Functional analysis Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Stochastic processes Hilbert space Banach spaces Radon-Nikodym property Functional analysis Stochastischer Prozess |
| url | https://doi.org/10.1142/11592 |
| work_keys_str_mv | AT kakiharayuichiro hilbertandbanachspacevaluedstochasticprocesses |