Approximation of Gaussian random elements and statistics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Stuttgart, [u.a.]
Teubner
1992
|
| Series: | Teubner-Texte zur Mathematik
Band 130 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 156 Seiten Illustrationen |
| ISBN: | 3815420296 |
Staff View
MARC
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| 100 | 1 | |a Richter, Matthias |d 1948- |0 (DE-588)1134896980 |4 aut | |
| 245 | 1 | 0 | |a Approximation of Gaussian random elements and statistics |c Matthias Richter |
| 264 | 1 | |a Stuttgart, [u.a.] |b Teubner |c 1992 | |
| 300 | |a 156 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Teubner-Texte zur Mathematik |v Band 130 | |
| 650 | 4 | |a Approximation stochastique | |
| 650 | 7 | |a Approximation, Théorie de l' |2 ram | |
| 650 | 4 | |a Elément aléatoire gaussien | |
| 650 | 4 | |a Statistique | |
| 650 | 4 | |a Système dynamique stochastique | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Gaussian processes | |
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Record in the Search Index
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Contents
0. Introduction 5
1. Gaussian random elements 8
1.1. Foundations and some notation 8
1.2. Gaussian random elements 12
1.3. Gaussian random elements with values in product spaces 17
1.4. H valued Wiener processes 19
1.5. Series representations of random processes 21
2. Gaussian statistical spaces 26
2.1. Foundations 26
2.2. Absolute continuity of Gaussian measures 28
2.3. Dominated Gaussian statistical spaces 30
2.3.1. Domination of particular Gaussian statistical spaces 30
2.3.2. Necessary and sufficient conditions of domination for
Gaussian statistical spaces by Gaussian measures 38
2.3.3. General case 43
2.3.4. Computation of the likelihood function of dominated
Gaussian statistical spaces 44
2.3.5. Identification of parameters of periodic processes 46
3. Quadratic forms of Gaussian random elements 48
3.1. Foundations 48
3.2. Moments of quadratic forms 56
3.3. Distribution function of finite dimensional positive
definite quadratic forms 61
3.3.1. Special cases 61
3.3.2. Inverting the characteristic function 64
3.3.3. Infinite series representations 65
3.3.4. Approximations by single distribution functions 66
3.3.5. Integral equations for Fn(x) 73
3.4. Infinite dimensional positive definite quadratic forms 77
3.4.1. Approximations 77
3.4.2. Special cases 83
3.4.3. Asymptotic behaviour 91
3.5. Some applications 91
3.5.1. Identification methods 91
3.5.2. Goodness of fit criteria 92
3
4. Approximation of random elements and statistics 93
4.1. Definitions and approximation criteria 93
4.2. Some properties for the approximation errors and risks 94
4.3. Approximation of real valued random processes 98
4.4. Approximation of Wiener processes 103
4.5. Approximation of statistics 108
4.5.1. Introduction 108
4.5.2. Sufficient approximations 108
4.5.3. Approximation of decision rules 110
4.5.4. Estimation of regression parameters 111
5. Optimal and admissible approximations 114
6.1. Problem formulation and assumptions 114
5.2. r optimal and r admissible operators 116
5.3. r optimal dimension for real valued Wiener processes 121
5.4. 1 optimal approximation operators 122
5.5. Principles of choicing suitable approximation operator
sequences 131
6. Some applications 137
6.1. Simulation of Gaussian random processes 137
6.2. Solution of stochastic differential equations 138
6.3. Identification of dynamical systems 139
Appendix 142
References " 145
Glossary of selected symbols 153
Subject index 156 |
| any_adam_object | 1 |
| author | Richter, Matthias 1948- |
| author_GND | (DE-588)1134896980 |
| author_facet | Richter, Matthias 1948- |
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| bvnumber | BV004715436 |
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| dewey-full | 519.5/42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/42 |
| dewey-search | 519.5/42 |
| dewey-sort | 3519.5 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004715436 |
| illustrated | Illustrated |
| indexdate | 2024-11-20T15:02:45Z |
| institution | BVB |
| isbn | 3815420296 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002897402 |
| oclc_num | 28066949 |
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| physical | 156 Seiten Illustrationen |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Teubner |
| record_format | marc |
| series | Teubner-Texte zur Mathematik |
| series2 | Teubner-Texte zur Mathematik |
| spelling | Richter, Matthias 1948- (DE-588)1134896980 aut Approximation of Gaussian random elements and statistics Matthias Richter Stuttgart, [u.a.] Teubner 1992 156 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Teubner-Texte zur Mathematik Band 130 Approximation stochastique Approximation, Théorie de l' ram Elément aléatoire gaussien Statistique Système dynamique stochastique Approximation theory Gaussian processes Approximation (DE-588)4002498-2 gnd rswk-swf Normalverteilung (DE-588)4075494-7 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Zufallsvariable (DE-588)4129514-6 gnd rswk-swf Gauß-Prozess (DE-588)4156111-9 gnd rswk-swf Normalverteilung (DE-588)4075494-7 s Zufallsvariable (DE-588)4129514-6 s Approximation (DE-588)4002498-2 s DE-604 Hilbert-Raum (DE-588)4159850-7 s Gauß-Prozess (DE-588)4156111-9 s Teubner-Texte zur Mathematik Band 130 (DE-604)BV000012607 130 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002897402&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Richter, Matthias 1948- Approximation of Gaussian random elements and statistics Teubner-Texte zur Mathematik Approximation stochastique Approximation, Théorie de l' ram Elément aléatoire gaussien Statistique Système dynamique stochastique Approximation theory Gaussian processes Approximation (DE-588)4002498-2 gnd Normalverteilung (DE-588)4075494-7 gnd Hilbert-Raum (DE-588)4159850-7 gnd Zufallsvariable (DE-588)4129514-6 gnd Gauß-Prozess (DE-588)4156111-9 gnd |
| subject_GND | (DE-588)4002498-2 (DE-588)4075494-7 (DE-588)4159850-7 (DE-588)4129514-6 (DE-588)4156111-9 |
| title | Approximation of Gaussian random elements and statistics |
| title_auth | Approximation of Gaussian random elements and statistics |
| title_exact_search | Approximation of Gaussian random elements and statistics |
| title_full | Approximation of Gaussian random elements and statistics Matthias Richter |
| title_fullStr | Approximation of Gaussian random elements and statistics Matthias Richter |
| title_full_unstemmed | Approximation of Gaussian random elements and statistics Matthias Richter |
| title_short | Approximation of Gaussian random elements and statistics |
| title_sort | approximation of gaussian random elements and statistics |
| topic | Approximation stochastique Approximation, Théorie de l' ram Elément aléatoire gaussien Statistique Système dynamique stochastique Approximation theory Gaussian processes Approximation (DE-588)4002498-2 gnd Normalverteilung (DE-588)4075494-7 gnd Hilbert-Raum (DE-588)4159850-7 gnd Zufallsvariable (DE-588)4129514-6 gnd Gauß-Prozess (DE-588)4156111-9 gnd |
| topic_facet | Approximation stochastique Approximation, Théorie de l' Elément aléatoire gaussien Statistique Système dynamique stochastique Approximation theory Gaussian processes Approximation Normalverteilung Hilbert-Raum Zufallsvariable Gauß-Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002897402&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012607 |
| work_keys_str_mv | AT richtermatthias approximationofgaussianrandomelementsandstatistics |