Linear processes in function spaces: theory and applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2000
|
| Series: | Lecture notes in statistics
149 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XIII, 283 S. graph. Darst. |
| ISBN: | 0387950524 9780387950525 |
Staff View
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| 650 | 7 | |a Statistiek |2 gtt | |
| 650 | 7 | |a Stochastische processen |2 gtt | |
| 650 | 7 | |a Waarschijnlijkheidstheorie |2 gtt | |
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Record in the Search Index
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| adam_text | D. BOSQ LINEAR PROCESSES IN FUNCTION SPACES THEORY AND APPLICATIONS
SPRINGER CONTENTS PREFACE VI NOTATION XI SYNOPSIS 1 1. THE OBJECT OF
STUDY 1 2. FINITE-DIMENSIONAL LINEAR PROCESSES 3 3. RANDOM VARIABLES IN
FUNCTION SPACES 5 4. LIMIT THEOREMS IN FUNCTION SPACES 7 5.
AUTOREGRESSIVE PROCESSES IN HILBERT SPACES 7 6. ESTIMATION OF COVARIANCE
OPERATORS 8 7. AUTOREGRESSIVE PROCESSES IN BANACH SPACES AND
REPRESENTATIONS OF CONTINUOUS-TIME PROCESSES 10 8. LINEAR PROCESSES IN
HILBERT SPACES AND BANACH SPACES 11 9. ESTIMATION OF AUTOCORRELATION
OPERATOR AND FORECASTING 12 10. APPLICATIONS 13 1. STOCHASTIC PROCESSES
AND RANDOM VARIABLES IN FUNCTION SPACES 15 1.1. STOCHASTIC PROCESSES 15
1.2. RANDOM FUNCTIONS 21 1.3. EXPECTATION AND CONDITIONAL EXPECTATION IN
BANACH SPACES 27 VIII CONTENTS 1.4. COVARIANCE OPERATORS AND
CHARACTERISTIC FUNCTIONALS IN BANACH SPACES . 30 1.5. RANDOM VARIABLES
AND OPERATORS IN HUBERT SPACES 33 1.6. LINEAR PREDICTION IN HUBERT
SPACES 38 NOTES 42 2. SEQUENCES OF RANDOM VARIABLES IN BANACH SPACES 4 3
2.1. STOCHASTIC PROCESSES AS SEQUENCES OF SS-VALUED RANDOM VARIABLES 43
2.2. CONVERGENCE OF SS-RANDOM VARIABLES 44 2.3. LIMIT THEOREMS FOR I.I.D.
SEQUENCES OF SS-RANDOM VARIABLES 47 2.4. SEQUENCES OF DEPENDENT RANDOM
VARIABLES IN BANACH SPACES 54 2.5. * DERIVATION OF EXPONENTIAL BOUNDS 66
NOTES 70 3. AUTOREGRESSIVE HILBERTIAN PROCESSES OF ORDER ONE 71 3.1.
STATIONARITY AND INNOVATION IN HUBERT SPACES 71 3.2. THE ARH(L) MODEL 73
3.3. BASIC PROPERTIES OF ARH(L) PROCESSES 79 3.4. ARH(L) PROCESSES WITH
SYMMETRIE COMPACT AUTOCORRELATION OPERATOR 82 3.5. LIMIT THEOREMS FOR
ARH(L) PROCESSES 86 NOTES 94 4. ESTIMATION OF AUTOCOVARIANCE OPERATORS
FOR ARH(L) PROCESSES 95 4.1. ESTIMATION OF THE COVARIANCE OPERATOR 95
4.2. ESTIMATION OF THE EIGENELEMENTS OF C 102 4.3. ESTIMATION OF THE
CROSS-COVARIANCE OPERATORS 112 4.4. LIMITS IN DISTRIBUTION 118 CONTENTS
IX NOTES 125 5. AUTOREGRESSIVE HILBERTIAN PROCESSES OF ORDER P 127 5.1.
THE ARH(P) MODEL 127 5.2. SECOND ORDER MOMENTS OF ARH(P) 133 5.3. LIMIT
THEOREMS FOR ARH(P) PROCESSE S 136 5.4. ESTIMATION OF AUTOCOVARIANCE OF
AN ARH(P) 140 5.5. ESTIMATION OF THE AUTOREGRESSION ORDER 143 NOTES 145
6. AUTOREGRESSIVE PROCESSES IN BANACH SPACES 147 1. STRONG
AUTOREGRESSIVE PROCESSES IN BANACH SPACES 147 2. AUTOREGRESSIVE
REPRESENTATION OF SOME REAL CONTINUOUS-TIME PROCESSES 150 3. LIMIT
THEOREMS 153 4. WEAK BANACH AUTOREGRESSIVE PROCESSES 161 5. ESTIMATION
OF AUTOCOVARIANCE 164 6. THE CASE OF C[0, 1] 168 7. SOME APPLICATIONS TO
REAL CONTINUOUS-TIME PROCESSES 175 NOTES 180 7. GENERAL LINEAR PROCESSES
IN FUNCTION SPACES 181 7.1. EXISTENCE AND FIRST PROPERTIES OF LINEAR
PROCESSES 182 7.2. INVERTIBILITY OF LINEAR PROCESSES 184 7.3. MARKOVIAN
REPRESENTATIONS OF LPH: APPLICATIONS 188 7.4. LIMIT THEOREMS FOR LPB AND
LPH 191 7.5. * DERIVATION OF INVERTIBILITY 195 NOTES 202 8. ESTIMATION
OF AUTOCORRELATION OPERATOR AND PREDICTION 203 8.1. ESTIMATION OF P IF H
IS FINITE DIMENSIONAL 204 8.2. ESTIMATION OF P IN A SPECIAL CASE 211 X
CONTENTS 8.3. THE GENERAL SITUATION 218 8.4. ESTIMATION OF
AUTOCORRELATION OPERATOR IN C[0,1] 222 8.5. STATISTICAL PREDICTION 226
8.6. * DERIVATION OF STRONG CONSISTENCY 229 NOTES 236 9. IMPLEMENTATION
OF FUNCTIONAL AUTOREGRESSIVE PREDICTORS AND NUMERICAL APPLICATIONS 237
9.1. FUNCTIONAL DATA 237 9.2. CHOOSING AND ESTIMATING A MODEL 240 9.3.
STATISTICAL METHODS OF PREDICTION 243 9.4. SOME NUMERICAL APPLICATIONS
247 NOTES 251 FIGURES 252 APPENDIX 263 1. MEASURE AND PROBABILITY 263 2.
RANDOM VARIABLES 264 3. FUNCTION SPACES 265 4. BASIC FUNCTION SPACES 266
5. CONDITIONAL EXPECTATION 267 6. STOCHASTIC INTEGRAL 267 REFERENCES 269
INDEX 277
|
| any_adam_object | 1 |
| author | Bosq, Denis 1939- |
| author_GND | (DE-588)172994314 |
| author_facet | Bosq, Denis 1939- |
| author_role | aut |
| author_sort | Bosq, Denis 1939- |
| author_variant | d b db |
| building | Verbundindex |
| bvnumber | BV013331906 |
| callnumber-first | Q - Science |
| callnumber-label | QA323 |
| callnumber-raw | QA323 |
| callnumber-search | QA323 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 237 SI 856 SK 820 |
| classification_tum | MAT 634f MAT 464f |
| ctrlnum | (OCoLC)44090528 (DE-599)BVBBV013331906 |
| dewey-full | 515/.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| indexdate | 2024-07-09T18:43:56Z |
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| isbn | 0387950524 9780387950525 |
| language | English |
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| physical | XIII, 283 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| publisher | Springer |
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| series | Lecture notes in statistics |
| series2 | Lecture notes in statistics |
| spelling | Bosq, Denis 1939- Verfasser (DE-588)172994314 aut Linear processes in function spaces theory and applications D. Bosq New York [u.a.] Springer 2000 XIII, 283 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics 149 Hier auch später erschienene, unveränderte Nachdrucke Espaces fonctionnels Espaces fonctionnels ram Functionaalanalyse gtt Operatortheorie gtt Processus stochastiques Processus stochastiques ram Statistiek gtt Stochastische processen gtt Waarschijnlijkheidstheorie gtt Statistik Function spaces Stochastic processes Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Funktionenraum (DE-588)4134834-5 gnd rswk-swf Funktionenraum (DE-588)4134834-5 s Stochastischer Prozess (DE-588)4057630-9 s Zeitreihenanalyse (DE-588)4067486-1 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4612-1154-9 Lecture notes in statistics 149 (DE-604)BV002447846 149 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009090587&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bosq, Denis 1939- Linear processes in function spaces theory and applications Lecture notes in statistics Espaces fonctionnels Espaces fonctionnels ram Functionaalanalyse gtt Operatortheorie gtt Processus stochastiques Processus stochastiques ram Statistiek gtt Stochastische processen gtt Waarschijnlijkheidstheorie gtt Statistik Function spaces Stochastic processes Zeitreihenanalyse (DE-588)4067486-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Funktionenraum (DE-588)4134834-5 gnd |
| subject_GND | (DE-588)4067486-1 (DE-588)4057630-9 (DE-588)4134834-5 |
| title | Linear processes in function spaces theory and applications |
| title_auth | Linear processes in function spaces theory and applications |
| title_exact_search | Linear processes in function spaces theory and applications |
| title_full | Linear processes in function spaces theory and applications D. Bosq |
| title_fullStr | Linear processes in function spaces theory and applications D. Bosq |
| title_full_unstemmed | Linear processes in function spaces theory and applications D. Bosq |
| title_short | Linear processes in function spaces |
| title_sort | linear processes in function spaces theory and applications |
| title_sub | theory and applications |
| topic | Espaces fonctionnels Espaces fonctionnels ram Functionaalanalyse gtt Operatortheorie gtt Processus stochastiques Processus stochastiques ram Statistiek gtt Stochastische processen gtt Waarschijnlijkheidstheorie gtt Statistik Function spaces Stochastic processes Zeitreihenanalyse (DE-588)4067486-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Funktionenraum (DE-588)4134834-5 gnd |
| topic_facet | Espaces fonctionnels Functionaalanalyse Operatortheorie Processus stochastiques Statistiek Stochastische processen Waarschijnlijkheidstheorie Statistik Function spaces Stochastic processes Zeitreihenanalyse Stochastischer Prozess Funktionenraum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009090587&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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