Holdings: An introduction to stochastic filtering theory

An introduction to stochastic filtering theory:

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Bibliographic Details
Main Author:	Xiong, Jie (Author)
Format:	Book
Language:	English
Published:	Oxford [u.a.] Oxford Univ. Press 2008
Edition:	1. publ.
Series:	Oxford graduate texts in mathematics 18
Subjects:	Stochastic processes Filters (Mathematics) Prediction theory Filterung > Stochastik
Online Access:	Inhaltsverzeichnis
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	XIII, 270 S.
ISBN:	9780199219704

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MARC


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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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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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