An introduction to stochastic filtering theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2008
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Oxford graduate texts in mathematics
18 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIII, 270 S. |
| ISBN: | 9780199219704 |
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Datensatz im Suchindex
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| adam_text | AN INTRODUCTION TO STOCHASTIC FILTERING THEORY JIE XIONG DEPARTMENT OF
MATHEMATICS UNIVERSITY OF TENNESSEE KNOXVILLE, TN 37996-1300, USA OXFORD
UNIVERSITY PRESS CONTENTS 1 INTRODUCTION 1.1 EXAMPLES 1 1.2 BASIC
DEFINITIONS AND THE FILTERING EQUATION 6 1.3 AN OVERVIEW 8 2 BROWNIAN
MOTION AND MARTINGALES 15 2.1 MARTINGALES 15 2.2 DOOB-MEYER
DECOMPOSITION 25 2.3 MEYER S PROCESSES 32 2.4 BROWNIAN MOTION 34 3
STOCHASTIC INTEGRALS AND ITO S FORMULA 36 3.1 PREDICTABLE PROCESSES 36
3.2 STOCHASTIC INTEGRAL 37 3.3 ITO S FORMULA 41 3.4 MARTINGALE
REPRESENTATION IN TERMS OF BROWNIAN MOTION 46 3.5 CHANGE OF MEASURES 52
3.6 STRATONOVICH INTEGRAL 57 4 STOCHASTIC DIFFERENTIAL EQUATIONS 61 4.1
BASIC DEFINITIONS 62 4.2 EXISTENCE AND UNIQUENESS OF A SOLUTION 67 4.3
MARTINGALE PROBLEM 70 4.4 A STOCHASTIC FLOW 72 4.5 MARKOV PROPERTY 79
XII CONTENTS 5 FILTERING MODEL AND KALLIANPUR-STRIEBEL FORMULA 82 5.1
5.2 5.3 5.4 5.5 THE FILTERING MODEL THE OPTIMAL FILTER FILTERING
EQUATION PARTICLE-SYSTEM REPRESENTATION NOTES UNIQUENESS OF THE SOLUTION
FOR ZAKAI S EQUATION 6.1 6.2 6.3 6.4 6.5 6.6 HILBERT SPACE
TRANSFORMATION TO A HILBERT SPACE SOME USEFUL INEQUALITIES UNIQUENESS
FOR ZAKAI S EQUATION A DUALITY REPRESENTATION NOTES UNIQUENESS OF THE
SOLUTION FOR THE FILTERING EQUATION 7.1 7.2 7.3 7.4 AN INTERACTING
PARTICLE SYSTEM THE UNIQUENESS OF THE SYSTEM UNIQUENESS FOR THE
FILTERING EQUATION NOTES NUMERICAL METHODS 8.1 8.2 8.3 8.4 8.5
MONTE-CARLO METHOD A BRANCHING PARTICLE SYSTEM CONVERGENCE OF V
CONVERGENCE OF V NOTES LINEAR FILTERING 9.1 9.2 9.3 9.4 GAUSSIAN SYSTEM
KALMAN-BUCY FILTERING DISCRETE-TIME APPROXIMATION OF THE KALMAN-BUCY
FILTERING SOME BASIC FACTS FOR A RELATED DETERMINISTIC CONTROL PROBLEM
82 83 86 93 95 96 96 98 103 109 111 120 121 121 124 129 131 132 132 137
143 149 155 157 157 160 164 165 CONTENTS 9.5 STABILITY FOR KALMAN-BUCY
FILTERING 180 9.6 NOTES 185 10 STABILITY OF NON-LINEAR FILTERING 186
10.1 MARKOV PROPERTY OF THE OPTIMAL FILTER 187 10.2 ERGODICITY OF THE
OPTIMAL FILTER 198 10.3 FINITE MEMORY PROPERTY 205 10.4 ASYMPTOTIC
STABILITY FOR NON-LINEAR FILTERING WITH COMPACT STATE SPACE 211 10.5
EXCHANGEABILITY OF UNION INTERSECTION FORA-FIELDS 223 10.6 NOTES 230 11
SINGULAR FILTERING 231 11.1 A SPECIAL EXAMPLE 231 11.2 A GENERAL
SINGULAR FILTERING MODEL 236 11.3 OPTIMAL FILTER WITH DISCRETE SUPPORT
240 11.4 OPTIMAL FILTER SUPPORTED ON MANIFOLDS 245 11.5 FILTERING MODEL
WITH ORNSTEIN-UHLENBECK NOISE 252 11.6 NOTES 254 BIBLIOGRAPHY 255 LIST
OF NOTATIONS 266 INDEX 269
|
| adam_txt |
AN INTRODUCTION TO STOCHASTIC FILTERING THEORY JIE XIONG DEPARTMENT OF
MATHEMATICS UNIVERSITY OF TENNESSEE KNOXVILLE, TN 37996-1300, USA OXFORD
UNIVERSITY PRESS CONTENTS 1 INTRODUCTION 1.1 EXAMPLES 1 1.2 BASIC
DEFINITIONS AND THE FILTERING EQUATION 6 1.3 AN OVERVIEW 8 2 BROWNIAN
MOTION AND MARTINGALES 15 2.1 MARTINGALES 15 2.2 DOOB-MEYER
DECOMPOSITION 25 2.3 MEYER'S PROCESSES 32 2.4 BROWNIAN MOTION 34 3
STOCHASTIC INTEGRALS AND ITO'S FORMULA 36 3.1 PREDICTABLE PROCESSES 36
3.2 STOCHASTIC INTEGRAL 37 3.3 ITO'S FORMULA 41 3.4 MARTINGALE
REPRESENTATION IN TERMS OF BROWNIAN MOTION 46 3.5 CHANGE OF MEASURES 52
3.6 STRATONOVICH INTEGRAL 57 4 STOCHASTIC DIFFERENTIAL EQUATIONS 61 4.1
BASIC DEFINITIONS 62 4.2 EXISTENCE AND UNIQUENESS OF A SOLUTION 67 4.3
MARTINGALE PROBLEM 70 4.4 A STOCHASTIC FLOW 72 4.5 MARKOV PROPERTY 79
XII CONTENTS 5 FILTERING MODEL AND KALLIANPUR-STRIEBEL FORMULA 82 5.1
5.2 5.3 5.4 5.5 THE FILTERING MODEL THE OPTIMAL FILTER FILTERING
EQUATION PARTICLE-SYSTEM REPRESENTATION NOTES UNIQUENESS OF THE SOLUTION
FOR ZAKAI'S EQUATION 6.1 6.2 6.3 6.4 6.5 6.6 HILBERT SPACE
TRANSFORMATION TO A HILBERT SPACE SOME USEFUL INEQUALITIES UNIQUENESS
FOR ZAKAI'S EQUATION A DUALITY REPRESENTATION NOTES UNIQUENESS OF THE
SOLUTION FOR THE FILTERING EQUATION 7.1 7.2 7.3 7.4 AN INTERACTING
PARTICLE SYSTEM THE UNIQUENESS OF THE SYSTEM UNIQUENESS FOR THE
FILTERING EQUATION NOTES NUMERICAL METHODS 8.1 8.2 8.3 8.4 8.5
MONTE-CARLO METHOD A BRANCHING PARTICLE SYSTEM CONVERGENCE OF V"
CONVERGENCE OF V" NOTES LINEAR FILTERING 9.1 9.2 9.3 9.4 GAUSSIAN SYSTEM
KALMAN-BUCY FILTERING DISCRETE-TIME APPROXIMATION OF THE KALMAN-BUCY
FILTERING SOME BASIC FACTS FOR A RELATED DETERMINISTIC CONTROL PROBLEM
82 83 86 93 95 96 96 98 103 109 111 120 121 121 124 129 131 132 132 137
143 149 155 157 157 160 164 165 CONTENTS 9.5 STABILITY FOR KALMAN-BUCY
FILTERING 180 9.6 NOTES 185 10 STABILITY OF NON-LINEAR FILTERING 186
10.1 MARKOV PROPERTY OF THE OPTIMAL FILTER 187 10.2 ERGODICITY OF THE
OPTIMAL FILTER 198 10.3 FINITE MEMORY PROPERTY 205 10.4 ASYMPTOTIC
STABILITY FOR NON-LINEAR FILTERING WITH COMPACT STATE SPACE 211 10.5
EXCHANGEABILITY OF UNION INTERSECTION FORA-FIELDS 223 10.6 NOTES 230 11
SINGULAR FILTERING 231 11.1 A SPECIAL EXAMPLE 231 11.2 A GENERAL
SINGULAR FILTERING MODEL 236 11.3 OPTIMAL FILTER WITH DISCRETE SUPPORT
240 11.4 OPTIMAL FILTER SUPPORTED ON MANIFOLDS 245 11.5 FILTERING MODEL
WITH ORNSTEIN-UHLENBECK NOISE 252 11.6 NOTES 254 BIBLIOGRAPHY 255 LIST
OF NOTATIONS 266 INDEX 269 |
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| index_date | 2024-07-02T21:01:28Z |
| indexdate | 2024-07-09T21:16:21Z |
| institution | BVB |
| isbn | 9780199219704 |
| language | English |
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| physical | XIII, 270 S. |
| publishDate | 2008 |
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| series | Oxford graduate texts in mathematics |
| series2 | Oxford graduate texts in mathematics |
| spelling | Xiong, Jie Verfasser aut An introduction to stochastic filtering theory Jie Xiong 1. publ. Oxford [u.a.] Oxford Univ. Press 2008 XIII, 270 S. txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts in mathematics 18 Hier auch später erschienene, unveränderte Nachdrucke Stochastic processes Filters (Mathematics) Prediction theory Filterung Stochastik (DE-588)4121267-8 gnd rswk-swf Filterung Stochastik (DE-588)4121267-8 s DE-604 Oxford graduate texts in mathematics 18 (DE-604)BV011416591 18 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016524242&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Xiong, Jie An introduction to stochastic filtering theory Oxford graduate texts in mathematics Stochastic processes Filters (Mathematics) Prediction theory Filterung Stochastik (DE-588)4121267-8 gnd |
| subject_GND | (DE-588)4121267-8 |
| title | An introduction to stochastic filtering theory |
| title_auth | An introduction to stochastic filtering theory |
| title_exact_search | An introduction to stochastic filtering theory |
| title_exact_search_txtP | An introduction to stochastic filtering theory |
| title_full | An introduction to stochastic filtering theory Jie Xiong |
| title_fullStr | An introduction to stochastic filtering theory Jie Xiong |
| title_full_unstemmed | An introduction to stochastic filtering theory Jie Xiong |
| title_short | An introduction to stochastic filtering theory |
| title_sort | an introduction to stochastic filtering theory |
| topic | Stochastic processes Filters (Mathematics) Prediction theory Filterung Stochastik (DE-588)4121267-8 gnd |
| topic_facet | Stochastic processes Filters (Mathematics) Prediction theory Filterung Stochastik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016524242&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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