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Gaussian processes:

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Bibliographic Details
Main Authors:	Hida, Takeyuki 1927-2017 (Author), Hitsuda, Masuyuki 1938- (Author)
Format:	Book
Language:	English Japanese
Published:	Providence, RI American Mathemat. Soc. 1993
Series:	Translations of mathematical monographs 120
Subjects:	Processus gaussiens Stochastische processen Gaussian processes Gauß-Prozess
Online Access:	Inhaltsverzeichnis
Item Description:	Aus d. Japan. übers.
Physical Description:	XV, 183 S.
ISBN:	0821845683 9780821843581

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MARC


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Record in the Search Index

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adam_text	Contents Preface to the English Edition vii Preface ix Introduction xi Chapter I. Foundations of Probability Theory and Limit Theorems 1 §1. Probability spaces and random variables 1 §2. Probability distributions of random variables (random vectors) and characteristic functions 3 §3. Convergence of sequences of random variables 6 §4. Limit theorems for sums of independent random variables 7 §5. Conditional expectations and martingales 8 §6. Measures on function spaces (measures induced from stochastic processes) 12 Chapter II. Systems of Gaussian Random Variables 15 §1. Definitions and preliminaries 15 §2. Some important properties of a Gaussian system 17 §3. Complex Gaussian systems 21 §4. Discrete parameter Gaussian processes: Canonical representation 25 §5. Continuous parameter Gaussian processes: Brownian motion 31 Chapter III. Stationary Gaussian Processes and Their Representations 37 §1. Discrete parameter stationary processes 37 §2. Spectral representation of a stationary Gaussian process 42 §3. Canonical representation of stationary processes I: The discrete parameter case 46 §4. Canonical representation of stationary processes II: The continuous parameter case 52 Chapter IV. Canonical Representation of Gaussian Processes: General Theory and Multiplicity 55 §1. Propagation of random phenomena 55 §2. Canonical representation and multiplicity 57 V vi CONTENTS §3. Gaussian processes and reproducing kernel Hilbert spaces 66 §4. Examples of a canonical representation and a noncanonical one 70 §5. Application to prediction theory 74 Chapter V. Multiple Markov Gaussian Processes 79 §1. Multiple Markov processes with discrete parameter 80 §2. Multiple Markov Gaussian processes with continuous parameter 83 §3. Multiple Markov Gaussian processes in the restricted sense 89 §4. Multiple Markov stationary Gaussian processes 100 §5. Levy s Af(*) process 107 §6. F positivity 116 Chapter VI. Equivalence of Gaussian Processes 121 §1. Setting up the problem 121 §2. General theory of equivalence of Gaussian measures 122 §3. Equivalence of Gaussian processes with discrete parameter 128 §4. Canonical representations of Gaussian processes equivalent to Wiener processes 131 §5. Canonical representation of Gaussian processes equivalent to a given Gaussian process 141 §6. Constructing innovation processes 143 Appendix. Stochastic Integrals and Martingales 149 §1. Multiple Wiener integrals 149 §2. Martingales and stochastic (Ito) integrals 156 §3. Ito s formula and Girsanov s theorem 165 Historical Notes 171 References 177 Subject Index 181
any_adam_object	1
author	Hida, Takeyuki 1927-2017 Hitsuda, Masuyuki 1938-
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indexdate	2024-07-09T17:15:33Z
institution	BVB
isbn	0821845683 9780821843581
language	English Japanese
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-005384710
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physical	XV, 183 S.
publishDate	1993
publishDateSearch	1993
publishDateSort	1993
publisher	American Mathemat. Soc.
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series	Translations of mathematical monographs
series2	Translations of mathematical monographs
spelling	Hida, Takeyuki 1927-2017 Verfasser (DE-588)124605257 aut Gausu-katei Gaussian processes Takeyuki Hida ; Masuyuki Hitsuda Providence, RI American Mathemat. Soc. 1993 XV, 183 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 120 Aus d. Japan. übers. Processus gaussiens Processus gaussiens ram Stochastische processen gtt Gaussian processes Gauß-Prozess (DE-588)4156111-9 gnd rswk-swf Gauß-Prozess (DE-588)4156111-9 s DE-604 Hitsuda, Masuyuki 1938- Verfasser (DE-588)172615399 aut Translations of mathematical monographs 120 (DE-604)BV000002394 120 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005384710&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Hida, Takeyuki 1927-2017 Hitsuda, Masuyuki 1938- Gaussian processes Translations of mathematical monographs Processus gaussiens Processus gaussiens ram Stochastische processen gtt Gaussian processes Gauß-Prozess (DE-588)4156111-9 gnd
subject_GND	(DE-588)4156111-9
title	Gaussian processes
title_alt	Gausu-katei
title_auth	Gaussian processes
title_exact_search	Gaussian processes
title_full	Gaussian processes Takeyuki Hida ; Masuyuki Hitsuda
title_fullStr	Gaussian processes Takeyuki Hida ; Masuyuki Hitsuda
title_full_unstemmed	Gaussian processes Takeyuki Hida ; Masuyuki Hitsuda
title_short	Gaussian processes
title_sort	gaussian processes
topic	Processus gaussiens Processus gaussiens ram Stochastische processen gtt Gaussian processes Gauß-Prozess (DE-588)4156111-9 gnd
topic_facet	Processus gaussiens Stochastische processen Gaussian processes Gauß-Prozess
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005384710&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000002394
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