High risk scenarios and extremes: a geometric approach
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Zürich
European Mathematical Soc.
2007
|
| Schriftenreihe: | Zurich lectures in Advanced Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 375 S. |
| ISBN: | 9783037190357 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804136457311354880 |
|---|---|
| adam_text | GUUS BALKEMA PAUL EMBRECHTS HIGH RISK SCENARIOS AND EXTREMES A GEOMETRIC
APPROACH UROPEAN^VTATHEMATICAL VJBCIETY CONTENTS FOREWORD VII
INTRODUCTION * . . 1 PREVIEW 13 A RECIPE 13 CONTENTS 31 NOTATION 36 I
POINT PROCESSES 41 1 AN INTUITIVE APPROACH 41 1.1 ABRIEF SHOWER 41 1.2
SAMPLE CLOUD MIXTURES 43 1.3 RANDOM SETS AND RANDOM MEASURES 44 1.4 THE
MEAN MEASURE 45 1.5* ENUMERATING THE POINTS 46 1.6 DEFINITIONS 47 2
POISSON POINT PROCESSES 48 2.1 POISSON MIXTURES OF SAMPLE CLOUDS 48 2.2
THE DISTRIBUTION OF A POINT PROCESS 49 2.3 DEFINITION OF THE POISSON
POINT PROCESS 50 2.4 VARIANCE AND COVARIANCE 51 2.5* THE BIVARIATE MEAN
MEASURE 52 2.6 LEVY PROCESSES 54 2.7 SUPERPOSITIONS OF ZERO-ONE POINT
PROCESSES 56 2.8 MAPPINGS 58 2.9* INVERSE MAPS 58 2.10* MARKED POINT
PROCESSES 62 3 THE DISTRIBUTION 63 3.1 INTRODUCTION 63 3.2* THE LAPLACE
TRANSFORM 64 3.3 THE DISTRIBUTION 65 3.4* THE DISTRIBUTION OF SIMPLE
POINT PROCESSES 67 4 CONVERGENCE 69 4.1 INTRODUCTION 69 4.2 THE STATE
SPACE 70 4.3 WEAK CONVERGENCE OF PROBABILITY MEASURES ON METRIC SPACES .
72 STARRED SECTIONS MAY BE SKIPPED ON A FIRST READING. X CONTENTS 4.4
RADON MEASURES AND VAGUE CONVERGENCE 76 4.5 CONVERGENCE OF POINT
PROCESSES 78 5 CONVERGING SAMPLE CLOUDS 81 5.1 INTRODUCTION 81 5.2
CONVERGENCE OF CONVEX HULLS, AN EXAMPLE 83 5.3 HALFSPACES, CONVEX SETS
AND CONES 84 5.4 THE INTRUSION CONE 87 5.5 THE CONVERGENCE CONE 89 5.6*
THE SUPPORT FUNCTION 92 5.7 ALMOST-SURE CONVERGENCE OF THE CONVEX HULLS
93 5.8 CONVERGENCE TO THE MEAN MEASURE 96 II MAXIMA 100 6 THE UNIVARIATE
THEORY: MAXIMA AND EXCEEDANCES 100 6.1 MAXIMA 100 6.2 EXCEEDANCES 101
6.3 THE DOMAIN OF THE EXPONENTIAL LAW 101 6.4 THE POISSON POINT PROCESS
ASSOCIATED WITH THE LIMIT LAW . . . . 102 6.5* MONOTONE TRANSFORMATIONS
104 6.6* THE VON MISES CONDITION 105 6.7* SELF-NEGLECTING FUNCTIONS 108
7 COMPONENTWISE MAXIMA 110 7.1 MAX-ID VECTORS 111 7.2 MAX-STABLE
VECTORS, THE STABILITY RELATIONS 112 7.3 MAX-STABLE VECTORS, DEPENDENCE
114 7.4 MAX-STABLE DISTRIBUTIONS WITH EXPONENTIAL MARGINALS ON(-OO,0)
117 7.5* MAX-STABLE DISTRIBUTIONS UNDER MONOTONE TRANSFORMATIONS . . 119
7.6 COMPONENTWISE MAXIMA AND COPULAS 121 III HIGH RISK LIMIT LAWS 123 8
HIGH RISK SCENARIOS 123 8.1 INTRODUCTION 123 8.2 THE LIMIT RELATION 125
8.3 THE MULTIVARIATE GAUSSIAN DISTRIBUTION 126 8.4 THE UNIFORM
DISTRIBUTION ON A BALL 128 8.5 HEAVY TAILS, RETURNS AND VOLATILITY IN
THE DAX 130 8.6 SOME BASIC THEORY 131 9 THE GAUSS-EXPONENTIAL DOMAIN,
ROTUND SETS 135 9.1 INTRODUCTION 136 CONTENTS XI 9.2 ROTUND SETS 138 9.3
INITIAL TRANSFORMATIONS 140 9.4 CONVERGENCE OF THE QUOTIENTS 143 9.5
GLOBAL BEHAVIOUR OF THE SAMPLE CLOUD 146 10 THE GAUSS-EXPONENTIAL
DOMAIN, UNIMODAL DISTRIBUTIONS 147 10.1 UNIMODALITY 147 10.2* CAPS 149
10.3* L 1 -CONVERGENCE OFDENSITIES 152 10.4 CONCLUSION 154 11 FIAT
FUNCTIONS AND FLAT MEASURES 156 11.1 FIAT FUNCTIONS . 156 11.2
MULTIVARIATE SLOW VARIATION 157 11.3 INTEGRABILITY 159 11.4* THEGEOMETRY
160 11.5 EXCESS FUNCTIONS 166 11.6* FIAT MEASURES 167 12 HEAVY TAILS AND
BOUNDED VECTORS 170 12.1 HEAVY TAILS 170 12.2 BOUNDED LIMIT VECTORS 173
13 THE MULTIVARIATE GPDS 176 13.1 A CONTINUOUS FAMILY OF LIMIT LAWS 176
13.2 SPHERICAL DISTRIBUTIONS 178 13.3 THE EXCESS MEASURES AND THEIR
SYMMETRIES 179 13.4 PROJECTION 180 13.5 INDEPENDENCE AND SPHERICAL
SYMMETRY 180 IV THRESHOLDS 182 14 EXCEEDANCES OVER HORIZONTAL THRESHOLDS
183 14.1 INTRODUCTION 183 14.2 CONVERGENCE OF THE VERTICAL COMPONENT 185
14.3* A FUNCTIONAL RELATION FOR THE LIMIT LAW 186 14.4* TAIL
SELF-SIMILAR DISTRIBUTIONS 187 14.5* DOMAINS OF ATTRACTION 190 14.6 THE
EXTENSION THEOREM 192 14.7 SYMMETRIES 193 14.8 THE REPRESENTATION
THEOREM 195 14.9 THE GENERATORS IN DIMENSION D = 3 AND DENSITIES 196
14.10 PROJECTIONS 198 14.11 STURDY MEASURES AND STEADY DISTRIBUTIONS 200
14.12 SPECTRAL STABILITY 203 14.13 EXCESS MEASURES FOR HORIZONTAL
THRESHOLDS 204 XII CONTENTS 14.14 NORMALIZING CURVES AND TYPICAL
DISTRIBUTIONS 205 14.15 APPROXIMATION BY TYPICAL DISTRIBUTIONS 209 15
HORIZONTAL THRESHOLDS - EXAMPLES 211 15.1 DOMAINS FOR EXCEEDANCES OVER
HORIZONTAL THRESHOLDS 211 15.2 VERTICAL TRANSLATIONS 211 15.3 CONES AND
VERTICES 218 15.4 CONES AND HEAVY TAILS 222 15.5* REGULAER VARIATION FOR
MATRICES IN A H 227 16 HEAVY TAILS AND ELLIPTIC THRESHOLDS 230 16.1
INTRODUCTION 230 16.2 THE EXCESS MEASURE 235 16.3 DOMAINS OF ELLIPTIC
ATTRACTION 240 16.4 CONVEX HULLS AND CONVERGENCE 243 16.5 TYPICAL
DENSITIES 245 16.6 ROUGHENING AND VAGUE CONVERGENCE 247 16.7 A
CHARACTERIZATION 251 16.8* INTERPOLATION OF ELLIPSOIDS, AND TWISTING 256
16.9 SPECTRAL DECOMPOSITION, THE BASIC RESULT 258 17 HEAVY TAILS -
EXAMPLES 263 17.1 SCALAR NORMALIZATION 264 17.2 SCALAR SYMMETRIES 268
17.3* COORDINATE BOXES 273 17.4 HEAVY AND HEAVIER TAILS 275 17.5*
MAXIMAL SYMMETRY 278 17.6* STABLE DISTRIBUTIONS AND PROCESSES 282 17.7*
ELLIPTIC THRESHOLDS 285 18 REGULAER VARIATION AND EXCESS MEASURES 295
18.1 REGULAER VARIATION 295 18.2 DISCRETE SKELETONS 299 18.3* REGULAER
VARIATION IN A + 300 18.4 THE MEERSCHAERT SPECTRAL DECOMPOSITION 304
18.5 LIMIT THEORY WITH REGULAER VARIATION 312 18.6 SYMMETRIES 314 18.7*
INVARIANT SETS AND HYPERPLANES 316 18.8 EXCESS MEASURES ON THE PLANE 318
18.9 ORBITS 320 18.10* UNIQUENESS OF EXTENSIONS 326 18.11* LOCAL
SYMMETRIES 329 18.12 JORDAN FORM AND SPECTRAL DECOMPOSITIONS 333 18.13
LIE GROUPS AND LIE ALGEBRAS 336 18.14 ANEXAMPLE 344 CONTENTS XIII V OPEN
PROBLEMS 348 19 THE STOCHASTIC MODEL 349 20 THE STATISTICAL ANALYSIS 356
BIBHOGRAPHY 361 INDEX 369
|
| adam_txt |
GUUS BALKEMA PAUL EMBRECHTS HIGH RISK SCENARIOS AND EXTREMES A GEOMETRIC
APPROACH UROPEAN^VTATHEMATICAL VJBCIETY CONTENTS FOREWORD VII
INTRODUCTION * . . 1 PREVIEW 13 A RECIPE 13 CONTENTS 31 NOTATION 36 I
POINT PROCESSES 41 1 AN INTUITIVE APPROACH 41 1.1 ABRIEF SHOWER 41 1.2
SAMPLE CLOUD MIXTURES 43 1.3 RANDOM SETS AND RANDOM MEASURES 44 1.4 THE
MEAN MEASURE 45 1.5* ENUMERATING THE POINTS 46 1.6 DEFINITIONS 47 2
POISSON POINT PROCESSES 48 2.1 POISSON MIXTURES OF SAMPLE CLOUDS 48 2.2
THE DISTRIBUTION OF A POINT PROCESS 49 2.3 DEFINITION OF THE POISSON
POINT PROCESS 50 2.4 VARIANCE AND COVARIANCE 51 2.5* THE BIVARIATE MEAN
MEASURE 52 2.6 LEVY PROCESSES 54 2.7 SUPERPOSITIONS OF ZERO-ONE POINT
PROCESSES 56 2.8 MAPPINGS 58 2.9* INVERSE MAPS 58 2.10* MARKED POINT
PROCESSES 62 3 THE DISTRIBUTION 63 3.1 INTRODUCTION 63 3.2* THE LAPLACE
TRANSFORM 64 3.3 THE DISTRIBUTION 65 3.4* THE DISTRIBUTION OF SIMPLE
POINT PROCESSES 67 4 CONVERGENCE 69 4.1 INTRODUCTION 69 4.2 THE STATE
SPACE 70 4.3 WEAK CONVERGENCE OF PROBABILITY MEASURES ON METRIC SPACES .
72 STARRED SECTIONS MAY BE SKIPPED ON A FIRST READING. X CONTENTS 4.4
RADON MEASURES AND VAGUE CONVERGENCE 76 4.5 CONVERGENCE OF POINT
PROCESSES 78 5 CONVERGING SAMPLE CLOUDS 81 5.1 INTRODUCTION 81 5.2
CONVERGENCE OF CONVEX HULLS, AN EXAMPLE 83 5.3 HALFSPACES, CONVEX SETS
AND CONES 84 5.4 THE INTRUSION CONE 87 5.5 THE CONVERGENCE CONE 89 5.6*
THE SUPPORT FUNCTION 92 5.7 ALMOST-SURE CONVERGENCE OF THE CONVEX HULLS
93 5.8 CONVERGENCE TO THE MEAN MEASURE 96 II MAXIMA 100 6 THE UNIVARIATE
THEORY: MAXIMA AND EXCEEDANCES 100 6.1 MAXIMA 100 6.2 EXCEEDANCES 101
6.3 THE DOMAIN OF THE EXPONENTIAL LAW 101 6.4 THE POISSON POINT PROCESS
ASSOCIATED WITH THE LIMIT LAW . . . . 102 6.5* MONOTONE TRANSFORMATIONS
104 6.6* THE VON MISES CONDITION 105 6.7* SELF-NEGLECTING FUNCTIONS 108
7 COMPONENTWISE MAXIMA 110 7.1 MAX-ID VECTORS 111 7.2 MAX-STABLE
VECTORS, THE STABILITY RELATIONS 112 7.3 MAX-STABLE VECTORS, DEPENDENCE
114 7.4 MAX-STABLE DISTRIBUTIONS WITH EXPONENTIAL MARGINALS ON(-OO,0)
117 7.5* MAX-STABLE DISTRIBUTIONS UNDER MONOTONE TRANSFORMATIONS . . 119
7.6 COMPONENTWISE MAXIMA AND COPULAS 121 III HIGH RISK LIMIT LAWS 123 8
HIGH RISK SCENARIOS 123 8.1 INTRODUCTION 123 8.2 THE LIMIT RELATION 125
8.3 THE MULTIVARIATE GAUSSIAN DISTRIBUTION 126 8.4 THE UNIFORM
DISTRIBUTION ON A BALL 128 8.5 HEAVY TAILS, RETURNS AND VOLATILITY IN
THE DAX 130 8.6 SOME BASIC THEORY 131 9 THE GAUSS-EXPONENTIAL DOMAIN,
ROTUND SETS 135 9.1 INTRODUCTION 136 CONTENTS XI 9.2 ROTUND SETS 138 9.3
INITIAL TRANSFORMATIONS 140 9.4 CONVERGENCE OF THE QUOTIENTS 143 9.5
GLOBAL BEHAVIOUR OF THE SAMPLE CLOUD 146 10 THE GAUSS-EXPONENTIAL
DOMAIN, UNIMODAL DISTRIBUTIONS 147 10.1 UNIMODALITY 147 10.2* CAPS 149
10.3* L 1 -CONVERGENCE OFDENSITIES 152 10.4 CONCLUSION 154 11 FIAT
FUNCTIONS AND FLAT MEASURES 156 11.1 FIAT FUNCTIONS . 156 11.2
MULTIVARIATE SLOW VARIATION 157 11.3 INTEGRABILITY 159 11.4* THEGEOMETRY
160 11.5 EXCESS FUNCTIONS 166 11.6* FIAT MEASURES 167 12 HEAVY TAILS AND
BOUNDED VECTORS 170 12.1 HEAVY TAILS 170 12.2 BOUNDED LIMIT VECTORS 173
13 THE MULTIVARIATE GPDS 176 13.1 A CONTINUOUS FAMILY OF LIMIT LAWS 176
13.2 SPHERICAL DISTRIBUTIONS 178 13.3 THE EXCESS MEASURES AND THEIR
SYMMETRIES 179 13.4 PROJECTION 180 13.5 INDEPENDENCE AND SPHERICAL
SYMMETRY 180 IV THRESHOLDS 182 14 EXCEEDANCES OVER HORIZONTAL THRESHOLDS
183 14.1 INTRODUCTION 183 14.2 CONVERGENCE OF THE VERTICAL COMPONENT 185
14.3* A FUNCTIONAL RELATION FOR THE LIMIT LAW 186 14.4* TAIL
SELF-SIMILAR DISTRIBUTIONS 187 14.5* DOMAINS OF ATTRACTION 190 14.6 THE
EXTENSION THEOREM 192 14.7 SYMMETRIES 193 14.8 THE REPRESENTATION
THEOREM 195 14.9 THE GENERATORS IN DIMENSION D = 3 AND DENSITIES 196
14.10 PROJECTIONS 198 14.11 STURDY MEASURES AND STEADY DISTRIBUTIONS 200
14.12 SPECTRAL STABILITY 203 14.13 EXCESS MEASURES FOR HORIZONTAL
THRESHOLDS 204 XII CONTENTS 14.14 NORMALIZING CURVES AND TYPICAL
DISTRIBUTIONS 205 14.15 APPROXIMATION BY TYPICAL DISTRIBUTIONS 209 15
HORIZONTAL THRESHOLDS - EXAMPLES 211 15.1 DOMAINS FOR EXCEEDANCES OVER
HORIZONTAL THRESHOLDS 211 15.2 VERTICAL TRANSLATIONS 211 15.3 CONES AND
VERTICES 218 15.4 CONES AND HEAVY TAILS 222 15.5* REGULAER VARIATION FOR
MATRICES IN A H 227 16 HEAVY TAILS AND ELLIPTIC THRESHOLDS 230 16.1
INTRODUCTION 230 16.2 THE EXCESS MEASURE 235 16.3 DOMAINS OF ELLIPTIC
ATTRACTION 240 16.4 CONVEX HULLS AND CONVERGENCE 243 16.5 TYPICAL
DENSITIES 245 16.6 ROUGHENING AND VAGUE CONVERGENCE 247 16.7 A
CHARACTERIZATION 251 16.8* INTERPOLATION OF ELLIPSOIDS, AND TWISTING 256
16.9 SPECTRAL DECOMPOSITION, THE BASIC RESULT 258 17 HEAVY TAILS -
EXAMPLES 263 17.1 SCALAR NORMALIZATION 264 17.2 SCALAR SYMMETRIES 268
17.3* COORDINATE BOXES 273 17.4 HEAVY AND HEAVIER TAILS 275 17.5*
MAXIMAL SYMMETRY 278 17.6* STABLE DISTRIBUTIONS AND PROCESSES 282 17.7*
ELLIPTIC THRESHOLDS 285 18 REGULAER VARIATION AND EXCESS MEASURES 295
18.1 REGULAER VARIATION 295 18.2 DISCRETE SKELETONS 299 18.3* REGULAER
VARIATION IN A + 300 18.4 THE MEERSCHAERT SPECTRAL DECOMPOSITION 304
18.5 LIMIT THEORY WITH REGULAER VARIATION 312 18.6 SYMMETRIES 314 18.7*
INVARIANT SETS AND HYPERPLANES 316 18.8 EXCESS MEASURES ON THE PLANE 318
18.9 ORBITS 320 18.10* UNIQUENESS OF EXTENSIONS 326 18.11* LOCAL
SYMMETRIES 329 18.12 JORDAN FORM AND SPECTRAL DECOMPOSITIONS 333 18.13
LIE GROUPS AND LIE ALGEBRAS 336 18.14 ANEXAMPLE 344 CONTENTS XIII V OPEN
PROBLEMS 348 19 THE STOCHASTIC MODEL 349 20 THE STATISTICAL ANALYSIS 356
BIBHOGRAPHY 361 INDEX 369 |
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| author | Balkema, Guus Embrechts, Paul 1953- |
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| building | Verbundindex |
| bvnumber | BV022396980 |
| classification_rvk | SK 820 SK 840 SK 980 |
| classification_tum | MAT 627f |
| ctrlnum | (OCoLC)254223205 (DE-599)BVBBV022396980 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV022396980 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T17:16:53Z |
| indexdate | 2024-07-09T20:56:42Z |
| institution | BVB |
| isbn | 9783037190357 |
| language | German |
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| owner | DE-824 DE-20 DE-91G DE-BY-TUM DE-N2 DE-11 DE-523 DE-19 DE-BY-UBM DE-384 DE-83 |
| owner_facet | DE-824 DE-20 DE-91G DE-BY-TUM DE-N2 DE-11 DE-523 DE-19 DE-BY-UBM DE-384 DE-83 |
| physical | XIII, 375 S. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | European Mathematical Soc. |
| record_format | marc |
| series2 | Zurich lectures in Advanced Mathematics |
| spelling | Balkema, Guus Verfasser aut High risk scenarios and extremes a geometric approach Guus Balkema ; Paul Embrechts Zürich European Mathematical Soc. 2007 XIII, 375 S. txt rdacontent n rdamedia nc rdacarrier Zurich lectures in Advanced Mathematics Risikomanagement (DE-588)4121590-4 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Extremwertstatistik (DE-588)4153429-3 gnd rswk-swf Extremwertstatistik (DE-588)4153429-3 s Multivariate Analyse (DE-588)4040708-1 s Risikomanagement (DE-588)4121590-4 s DE-604 Embrechts, Paul 1953- Verfasser (DE-588)115254447 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015605701&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Balkema, Guus Embrechts, Paul 1953- High risk scenarios and extremes a geometric approach Risikomanagement (DE-588)4121590-4 gnd Multivariate Analyse (DE-588)4040708-1 gnd Extremwertstatistik (DE-588)4153429-3 gnd |
| subject_GND | (DE-588)4121590-4 (DE-588)4040708-1 (DE-588)4153429-3 |
| title | High risk scenarios and extremes a geometric approach |
| title_auth | High risk scenarios and extremes a geometric approach |
| title_exact_search | High risk scenarios and extremes a geometric approach |
| title_exact_search_txtP | High risk scenarios and extremes a geometric approach |
| title_full | High risk scenarios and extremes a geometric approach Guus Balkema ; Paul Embrechts |
| title_fullStr | High risk scenarios and extremes a geometric approach Guus Balkema ; Paul Embrechts |
| title_full_unstemmed | High risk scenarios and extremes a geometric approach Guus Balkema ; Paul Embrechts |
| title_short | High risk scenarios and extremes |
| title_sort | high risk scenarios and extremes a geometric approach |
| title_sub | a geometric approach |
| topic | Risikomanagement (DE-588)4121590-4 gnd Multivariate Analyse (DE-588)4040708-1 gnd Extremwertstatistik (DE-588)4153429-3 gnd |
| topic_facet | Risikomanagement Multivariate Analyse Extremwertstatistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015605701&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT balkemaguus highriskscenariosandextremesageometricapproach AT embrechtspaul highriskscenariosandextremesageometricapproach |