Filtering and prediction: a primer
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2007]
|
| Schriftenreihe: | Student mathematical library
volume 38 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis: Seite 247 |
| Beschreibung: | xi, 252 Seiten 22 cm |
| ISBN: | 9780821843338 0821843338 |
Internformat
MARC
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| 100 | 1 | |a Fristedt, Bert |d 1937- |e Verfasser |0 (DE-588)1145590519 |4 aut | |
| 245 | 1 | 0 | |a Filtering and prediction |b a primer |c B. Fristedt, N. Jain, N. Krylov |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2007] | |
| 264 | 4 | |c © 2007 | |
| 300 | |a xi, 252 Seiten |c 22 cm | ||
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| 650 | 4 | |a Processus de Markov | |
| 650 | 4 | |a Prévision, Théorie de la | |
| 650 | 4 | |a Markov processes | |
| 650 | 4 | |a Filters (Mathematics) | |
| 650 | 4 | |a Prediction theory | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface ix
Chapter 1. Preliminaries 1
§1. Series 2
1:1. Sums and series. 2
1:2. Some examples 7
1:3. The theorems of Fubini and Tonelli. 8
§2. Probability concepts 10
2:1. Random variables. 10
2:2. Expectations of real-valued random variables that
are not necessarily discrete 14
2:3. Second moments, variance, and standard deviation 15
2:4. Independence 16
2:5. Some important distributions 18
§3. Conditioning in the discrete case 19
3:1. Generalities. 19
3:2. Applications in estimating 29
Chapter 2. Markov chains 33
vi Contents
§1. Random walks 33
§2. Discrete time and space Markov chains 42
§3. Further problems on Markov chains 57
Chapter 3. Filtering of discrete Markov chains 61
§1. Filtering 63
§2. Parameter estimation for discrete Markov chains 72
§3. Interpolation for discrete Markov chains 80
3:1. Interpolation equation 80
3:2. Conjugate equations 87
3:3. Other problems related to interpolation 89
§4. Prediction for discrete Markov chains 92
Chapter 4. Conditional expectations 95
§1. Z 2-spaces 95
1:1. Case of finite fi 95
1:2. General case 104
§2. Definition of conditional expectations 108
2:1. General case 108
2:2. The case of Gaussian random variables 112
§3. Conditional expectations and densities 118
Chapter 5. Filtering of continuous-space Markov chains 127
§1. Filtering of Revalued Markov chains 127
§2. Discrete-time Kaiman filter 132
2:1. One-dimensional case 133
2:2. Multidimensional case 137
§3. Linear filtering 147
Chapter 6. Wiener process and continuous time filtering 161
Contents vii
§1. Introduction 161
§2. Definition and simplest properties of the Wiener process 162
§3. Integration against the Wiener process 168
§4. Recalling power series and systems of ODEs 172
§5. Kaiman filter in continuous time 179
Chapter 7. Stationary sequences 191
§1. Definition and simplest properties 191
§2. Spectral densities 197
§3. Filtering stationary sequences 204
§4. The Bochner-Khinchin theorem (optional) 207
§5. The law of large numbers (optional) 210
§6. Spectral representation of stationary sequences (optional) 213
Chapter 8. Prediction of stationary sequences 225
§1. Some properties of rational spectral densities 227
§2. Predicting one step ahead 233
§3. Predicting many steps ahead 240
§4. Dynamic predicting 243
Bibliography 247
Index 249
|
| adam_txt |
Contents
Preface ix
Chapter 1. Preliminaries 1
§1. Series 2
1:1. Sums and series. 2
1:2. Some examples 7
1:3. The theorems of Fubini and Tonelli. 8
§2. Probability concepts 10
2:1. Random variables. 10
2:2. Expectations of real-valued random variables that
are not necessarily discrete 14
2:3. Second moments, variance, and standard deviation 15
2:4. Independence 16
2:5. Some important distributions 18
§3. Conditioning in the discrete case 19
3:1. Generalities. 19
3:2. Applications in estimating 29
Chapter 2. Markov chains 33
vi Contents
§1. Random walks 33
§2. Discrete time and space Markov chains 42
§3. Further problems on Markov chains 57
Chapter 3. Filtering of discrete Markov chains 61
§1. Filtering 63
§2. Parameter estimation for discrete Markov chains 72
§3. Interpolation for discrete Markov chains 80
3:1. Interpolation equation 80
3:2. Conjugate equations 87
3:3. Other problems related to interpolation 89
§4. Prediction for discrete Markov chains 92
Chapter 4. Conditional expectations 95
§1. Z 2-spaces 95
1:1. Case of finite fi 95
1:2. General case 104
§2. Definition of conditional expectations 108
2:1. General case 108
2:2. The case of Gaussian random variables 112
§3. Conditional expectations and densities 118
Chapter 5. Filtering of continuous-space Markov chains 127
§1. Filtering of Revalued Markov chains 127
§2. Discrete-time Kaiman filter 132
2:1. One-dimensional case 133
2:2. Multidimensional case 137
§3. Linear filtering 147
Chapter 6. Wiener process and continuous time filtering 161
Contents vii
§1. Introduction 161
§2. Definition and simplest properties of the Wiener process 162
§3. Integration against the Wiener process 168
§4. Recalling power series and systems of ODEs 172
§5. Kaiman filter in continuous time 179
Chapter 7. Stationary sequences 191
§1. Definition and simplest properties 191
§2. Spectral densities 197
§3. Filtering stationary sequences 204
§4. The Bochner-Khinchin theorem (optional) 207
§5. The law of large numbers (optional) 210
§6. Spectral representation of stationary sequences (optional) 213
Chapter 8. Prediction of stationary sequences 225
§1. Some properties of rational spectral densities 227
§2. Predicting one step ahead 233
§3. Predicting many steps ahead 240
§4. Dynamic predicting 243
Bibliography 247
Index 249 |
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| index_date | 2024-07-02T20:14:37Z |
| indexdate | 2024-07-09T21:13:19Z |
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| language | English |
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| spelling | Fristedt, Bert 1937- Verfasser (DE-588)1145590519 aut Filtering and prediction a primer B. Fristedt, N. Jain, N. Krylov Providence, Rhode Island American Mathematical Society [2007] © 2007 xi, 252 Seiten 22 cm txt rdacontent n rdamedia nc rdacarrier Student mathematical library volume 38 Literaturverzeichnis: Seite 247 Filtres (Mathématiques) Processus de Markov Prévision, Théorie de la Markov processes Filters (Mathematics) Prediction theory Filter Mathematik (DE-588)4154388-9 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Markov-Prozess (DE-588)4134948-9 s DE-604 Filter Mathematik (DE-588)4154388-9 s Jain, Naresh 1937- Verfasser (DE-588)173966098 aut Krylov, Nikolaj V. 1941- Verfasser (DE-588)121699684 aut Erscheint auch als Online-Ausgabe 978-1-4704-1216-6 Student mathematical library volume 38 (DE-604)BV013184751 38 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016403342&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fristedt, Bert 1937- Jain, Naresh 1937- Krylov, Nikolaj V. 1941- Filtering and prediction a primer Student mathematical library Filtres (Mathématiques) Processus de Markov Prévision, Théorie de la Markov processes Filters (Mathematics) Prediction theory Filter Mathematik (DE-588)4154388-9 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| subject_GND | (DE-588)4154388-9 (DE-588)4134948-9 (DE-588)4123623-3 |
| title | Filtering and prediction a primer |
| title_auth | Filtering and prediction a primer |
| title_exact_search | Filtering and prediction a primer |
| title_exact_search_txtP | Filtering and prediction a primer |
| title_full | Filtering and prediction a primer B. Fristedt, N. Jain, N. Krylov |
| title_fullStr | Filtering and prediction a primer B. Fristedt, N. Jain, N. Krylov |
| title_full_unstemmed | Filtering and prediction a primer B. Fristedt, N. Jain, N. Krylov |
| title_short | Filtering and prediction |
| title_sort | filtering and prediction a primer |
| title_sub | a primer |
| topic | Filtres (Mathématiques) Processus de Markov Prévision, Théorie de la Markov processes Filters (Mathematics) Prediction theory Filter Mathematik (DE-588)4154388-9 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| topic_facet | Filtres (Mathématiques) Processus de Markov Prévision, Théorie de la Markov processes Filters (Mathematics) Prediction theory Filter Mathematik Markov-Prozess Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016403342&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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