Holdings: The Geometry of Filtering

The Geometry of Filtering:

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Bibliographic Details
Main Authors:	Elworthy, Kenneth David 1940- (Author), Le Jan, Yves 1952- (Author), Li, Xue-Mei 1964- (Author)
Format:	Book
Language:	English
Published:	Basel Birkhäuser 2010
Series:	Frontiers in Mathematics
Online Access:	Inhaltsverzeichnis
Physical Description:	XI, 169 S.
ISBN:	9783034601757

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MARC


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Record in the Search Index

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adam_text	IMAGE 1 CONTENTS INTRODUCTION VII 1 DIUSION OPERATORS 1 1.1 REPRESENTATIONS OF DIUSION OPERATORS . . . . . . . . . . . . . . . . 1 1.2 THE ASSOCIATED FIRST-ORDER OPERATOR . . . . . . . . . . . . . . . . . 4 1.3 DIUSION OPERATORS ALONG A DISTRIBUTION . . . . . . . . . . . . . . 5 1.4 LIFTS OF DIUSION OPERATORS . . . . . . . . . . . . . . . . . . . . . . 7 1.5 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 DECOMPOSITION OF DIUSION OPERATORS 11 2.1 THE HORIZONTAL LIFT MAP . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 LIFTS OF COHESIVE OPERATORS AND THE DECOMPOSITION THEOREM . . . 17 2.3 THE LIFT MAP FOR SDES AND DECOMPOSITION OF NOISE . . . . . . . . 23 2.3.1 DECOMPOSITION OF STRATONOVICH SDE S . . . . . . . . . . . . 24 2.3.2 DECOMPOSITION OF THE NOISE AND IT^ O SDE S . . . . . . . . . . 25 2.4 DIUSION OPERATORS WITH PROJECTIBLE SYMBOLS . . . . . . . . . . . . 26 2.5 HORIZONTAL LIFTS OF PATHS AND COMPLETENESS OF SEMI-CONNECTIONS . . . 28 2.6 TOPOLOGICAL IMPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . 30 2.7 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3 EQUIVARIANT DIUSIONS ON PRINCIPAL BUNDLES 33 3.1 INVARIANT SEMI-CONNECTIONS ON PRINCIPAL BUNDLES . . . . . . . . . . 34 3.2 DECOMPOSITIONS OF EQUIVARIANT OPERATORS . . . . . . . . . . . . . . 36 3.3 DERIVATIVE FLOWS AND ADJOINT CONNECTIONS . . . . . . . . . . . . . . 41 3.4 ASSOCIATED VECTOR BUNDLES AND GENERALISED WEITZENB OCK FORMULAE 46 3.5 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4 PROJECTIBLE DIUSION PROCESSES AND MARKOVIAN FILTERING 61 4.1 INTEGRATION OF PREDICTABLE PROCESSES . . . . . . . . . . . . . . . . . . 62 4.2 HORIZONTALITY AND LTRATIONS . . . . . . . . . . . . . . . . . . . . . . 66 4.3 INTERTWINED DIUSION PROCESSES . . . . . . . . . . . . . . . . . . . . 66 4.4 A FAMILY OF MARKOVIAN KERNELS . . . . . . . . . . . . . . . . . . . . . 70 IMAGE 2 VI CONTENTS 4.5 THE LTERING EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.6 APPROXIMATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.7 KRYLOV-VERETENNIKOV EXPANSION . . . . . . . . . . . . . . . . . . . . 74 4.8 CONDITIONAL LAWS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.9 AN SPDE EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.10 EQUIVARIANT CASE: SKEW-PRODUCT DECOMPOSITION . . . . . . . . . . . . 81 4.11 CONDITIONAL EXPECTATIONS OF INDUCED PROCESSES ON VECTOR BUNDLES . 83 4.12 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5 FILTERING WITH NON-MARKOVIAN OBSERVATIONS 87 5.1 SIGNALS WITH PROJECTIBLE SYMBOL . . . . . . . . . . . . . . . . . . . . 88 5.2 INNOVATIONS AND INNOVATIONS PROCESSES . . . . . . . . . . . . . . . . 91 5.3 CLASSICAL FILTERING . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.4 EXAMPLE: ANOTHER SPDE . . . . . . . . . . . . . . . . . . . . . . . 95 5.5 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6 THE COMMUTATION PROPERTY 101 6.1 COMMUTATIVITY OF DIUSION SEMIGROUPS . . . . . . . . . . . . . . . 103 6.2 CONSEQUENCES FOR THE HORIZONTAL FLOW . . . . . . . . . . . . . . . . 105 7 EXAMPLE: RIEMANNIAN SUBMERSIONS AND SYMMETRIC SPACES 115 7.1 RIEMANNIAN SUBMERSIONS . . . . . . . . . . . . . . . . . . . . . . . 115 7.2 RIEMANNIAN SYMMETRIC SPACES . . . . . . . . . . . . . . . . . . . . 116 7.3 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 8 EXAMPLE: STOCHASTIC FLOWS 121 8.1 SEMI-CONNECTIONS ON THE BUNDLE OF DIEOMORPHISMS . . . . . . . . 121 8.2 SEMI-CONNECTIONS INDUCED BY STOCHASTIC FLOWS . . . . . . . . . . . 125 8.3 SEMI-CONNECTIONS ON NATURAL BUNDLES . . . . . . . . . . . . . . . . . 131 9 APPENDICES 135 9.1 GIRSANOV-MARUYAMA-CAMERON-MARTIN THEOREM . . . . . . . . . . . 135 9.2 STOCHASTIC DIERENTIAL EQUATIONS FOR DEGENERATE DIUSIONS . . . . . . 139 9.3 SEMI-MARTINGALES AND -MARTINGALES ALONG A SUBBUNDLE . . . . . . 145 9.4 SECOND FUNDAMENTAL FORMS AND SHAPE OPERATORS . . . . . . . . . . . 147 9.5 INTERTWINED STOCHASTIC OWS . . . . . . . . . . . . . . . . . . . . . . 148 BIBLIOGRAPHY 159 INDEX 167
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author	Elworthy, Kenneth David 1940- Le Jan, Yves 1952- Li, Xue-Mei 1964-
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spellingShingle	Elworthy, Kenneth David 1940- Le Jan, Yves 1952- Li, Xue-Mei 1964- The Geometry of Filtering
title	The Geometry of Filtering
title_auth	The Geometry of Filtering
title_exact_search	The Geometry of Filtering
title_full	The Geometry of Filtering K. David Elworthy ; Yves LeJan ; Xue-Mei Li
title_fullStr	The Geometry of Filtering K. David Elworthy ; Yves LeJan ; Xue-Mei Li
title_full_unstemmed	The Geometry of Filtering K. David Elworthy ; Yves LeJan ; Xue-Mei Li
title_short	The Geometry of Filtering
title_sort	the geometry of filtering
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195520&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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