Gaussian processes:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English Japanese |
| Veröffentlicht: |
Providence, RI
American Mathemat. Soc.
1993
|
| Schriftenreihe: | Translations of mathematical monographs
120 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Japan. übers. |
| Beschreibung: | XV, 183 S. |
| ISBN: | 0821845683 9780821843581 |
Internformat
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| 240 | 1 | 0 | |a Gausu-katei |
| 245 | 1 | 0 | |a Gaussian processes |c Takeyuki Hida ; Masuyuki Hitsuda |
| 264 | 1 | |a Providence, RI |b American Mathemat. Soc. |c 1993 | |
| 300 | |a XV, 183 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Translations of mathematical monographs |v 120 | |
| 500 | |a Aus d. Japan. übers. | ||
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| 650 | 4 | |a Gaussian processes | |
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Datensatz im Suchindex
| _version_ | 1804122544147529728 |
|---|---|
| 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
|
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| author | Hida, Takeyuki 1927-2017 Hitsuda, Masuyuki 1938- |
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| classification_tum | MAT 603f |
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| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV008161885 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:15:33Z |
| institution | BVB |
| isbn | 0821845683 9780821843581 |
| language | English Japanese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005384710 |
| oclc_num | 26546750 |
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| physical | XV, 183 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | American Mathemat. Soc. |
| record_format | marc |
| 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 |
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