École d'Été de Probabilités de Saint-Flour XII - 1982:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Weitere Verfasser: | |
| Format: | Tagungsbericht Buch |
| Sprache: | English French |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1984
|
| Schriftenreihe: | Lecture notes in mathematics
1097 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 396 S. graph. Darst. |
| ISBN: | 3540138978 0387138978 |
Internformat
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| 245 | 1 | 0 | |a École d'Été de Probabilités de Saint-Flour XII - 1982 |c R. M. Dudley ; H. Kunita ; F. Ledrappier. Éd. par P. L. Hennequin |
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Datensatz im Suchindex
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|---|---|
| adam_text | TABLE DES MATIERES
R.H. DUDLEY : A COURSE ON EMPIRICAL PROCESSES
PREFACE 2
CHAPITRE 1 - INTRODUCTION
1.1 Invariance principles 6
1.2 Construction of joint distributions 8
CHAPITRE 2 - EMPIRICAL PROCESSES, GAUSSIAM LIMITS AMD INEQPALITIES
2.1 Gaussian limit processes 11
2.2 Inequalities 13
CHAPITRE 3 - MEASURABILITY AMD SUMS IN GENERAL BAMACH SPACES
3.1 Measurable cover functions and norms 17
3.2 Independent random éléments and partial sums 20
3.3 A central limit theorem implies measurability in separable
-Banach spaces 24
CHAPITRE 4 - ASYMPTOTIC EQTJICONTINPITY AND LIMIT THEOREMS
4.1 A eharacterization of functional Donsker classes 27
4.2 Strong invariance principles 32
CHAPITRE 5 - SEQUENCES OF SETS AMD FUNCTIONS
5.1 Séquences of sets 34
5.2 Séquences of functions 37
CHAPITRE 6 - METRIC EMTROPY, WITH IHCLTJSIOM AND BRACKETING
6.0 Me trie entropy and capacity 39
6. 1 Définitions and the Blmn-DeHardt law of large numbers 40
6.2 A central limit theorem for sets or bounded functions 44
6.3 The power set of a countable set : BORISÛV-DURST theorem 47
6.4 Central limit theorems for classes of unbounded functions 49
CHAPITRE 7 - APPROXIMATION OF FUNCTIOMS AMP SETS
7.0 Introduction ; the Hausdorff metric 50
7.! Spaces of differentiable functions and sets with
differentiable boundaries 51
7.2 Lower layers 57
7.3 Metric entropy of classes of convex sets 62
VIII
CHAPITRE 8 - CLASSES OF SETS OR FUNCTIONS TOO LARGE FOR CENTRAL
LIMIT THEOREMS
8.1 Universai lower bounds 68
8.2 An upper bound 70
8.3 Poissonization and random sets 72
8.4 Lower bounds in borderline cases 76
CHAPITRE 9 - VAPNIK-CERVONENKIS CLASSES
9.1 Introduction 81
9.2 Génération of classes and évaluation of S (%} 84
9.3 Vapnik-Cervonenkis classes, independence and probability laws 91
CHAPITRE 10 - MEASURABILITY CONSIDERATIONS :
10.1 Sufficiency 94
10.2 Admissibility 97
10.3 Suslin properties, sélection and a counter-example. 100
CHAPITRE 1 1 - LIMIT THEOREMS ON VAPNIK-CERVONENKIS CLASSES AND PSING
KOLCINSKII-POLLARP ENTROPY ,
11.1 Kolcinskii-Pollard entropy and Glivenko-Cantelli theorems 105
11.2 Vapnik-Cervonenkis-Steele laws of large numbers 11.1
11.3 Pollard s central limit theorem J17
11.4 Necessary conditions for limit theorems 125
CHAPITRE 12 - NON-PARAMETRie STATISTICS ANP SPEEDS OF CONVERGENCE j
12. 1 Non-parametric statistics 128
12.2 Speeds of convergence in central limit theorems 129
INDEX OF NOTATION AND TERMINOLOGY 131
REFERENCES 133
IX
H. KUNITA : STOCHASTIC DIFFERENTIAL EQUATIONS AND STOCHASTIC FLOW
OF DIFFEOMORPHISMS
INTRODUCTION 144
CHAPITRE I - STOCHASTIC CALCULUS FOR COHTINTJOUS SEMIMARTINGALES
1. Preliminaries 149
2. Quadratic variations of continuous semimartingales 153
3. Continuity of quadratic variations in M and M °C .160
4. Joint quadratic variations 163
5. Stochastic intégrais 166
6. Stochastic intégrais of vector vâlued processes 170
7. Regularity of intégrais with respect to parameters 176
8. Ito s formula 183
9. Brownian motions and stochastic intégrais 191
10. Appendix. Kolmogorov s theorem 195
CHAPITRE II - STOCHASTIC PIFFERENTIAL EQUATIOHS AMD STOCHASTIC FLOWS
OF HOMEOMORPHISMS
1. Stochastic differential équation with Lipschitz continuous
coefficients 206
2. Continuity of the solution with respect to the initial data 2]0
3. Smoothness of the solution with respect to the initial data 218
4. Stochastic flow of homeomorphisms (I). Case of globally
Lipschitz continuous coefficients 223
5. SDE with loçally Lipschitz continuous coefficients 228
6. Stochastic flow of homeomorphisms (II), A necessary and
sufficient condition 234
7. Stratonovich stochastic differential équations 238
8. Stochastic differential équations on manifold 243
9. Stochastic flow of homeomorphisms (III). Case of manifold 250
CHAPITRE III - DIFFEBENT1AL GEOMETRIC AMAIYSIS OF STOCHASTIC FLOWS
1. ItS s forward and backward formula for stochastic flows 255
2. Ito s formula for Ç aeting on vector fields 263
s j t
3. Composition and décomposition of the solution 268
4. Ito s formula for g aeting on tensor fields 276
5. Supports of stochastic flow of diffeomorphisms 281
6. ItS s formula for stochastic parallel displacement of
tensor fields 287
7. Application to paraholic partial differential équations 294
REFEREHCES 300
X ;
F. LEDRAPPIER - QUELQUES PROPRIETES DES EXPOSANTS CARACTERISTIQUES
y
PREFACE 306
CHAPITRE I - THEOREME ERGODIQUE MULTIPLICATIF D OSSELEDETS
1. Exposants caractéristiques 308
2. Théorème ergodique sous-additif 311
3. Théorème ergodique multiplicatif ¦ 316 ,
4. Cas inversible . 323
5. Mesures invariantes 328
CHAPITRE II ~ ENTROPIE ET EXPOSANTS
1. Entropie des systèmes dynamiques 330
2. Applications diffêrentiables 333
3. Théorème de Shannon - Me. Millan - Breiman 339
4. Minoration de la dimension 341
5. Exposants, entropie et dimension en dimension 2 347
6. Appendice au chapitre II : démonstration du léînme 5.5 355
CHAPITRE III - FAMILLES INDEPENDANTES
1. La formule de Fiïrstenberg pour À. 357
2. Entropie d un produit indépendant de matrices 362
3. Critère de Furstenberg 367
4. Majoration de la dimension de la mesure invariante 372
5. Exposant, entropie et dimension en dimension 2 377 ;
CHAPITRE IV - EXEMPLES
1. Spectre singulier des opérateurs de Schrodinger aléatoires.
L argument de Pastour 382
2. Marche aléatoire sur Z dans un milieu aléatoire 387
3. Appendice. Démonstration de la proposition 2.1 394 !
REFERENCES GENERALES ¦ 396
(une brève notice bibliographique termine aussi chaque paragraphe) :
|
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| spelling | Dudley, Richard M. 1938- Verfasser (DE-588)121010996 aut École d'Été de Probabilités de Saint-Flour XII - 1982 R. M. Dudley ; H. Kunita ; F. Ledrappier. Éd. par P. L. Hennequin Berlin [u.a.] Springer 1984 X, 396 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1097 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Saint-Flour <1982> gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Saint-Flour <1982> f DE-604 Kunita, H. 1937-2019 Verfasser (DE-588)1055753419 aut Ledrappier, François Verfasser aut Hennequin, Paul L. (DE-588)1067948570 edt Ecole d'Eté de Probabilités 12 1982 Saint-Flour Sonstige (DE-588)1092819-4 oth Lecture notes in mathematics 1097 (DE-604)BV000676446 1097 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018334254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dudley, Richard M. 1938- Kunita, H. 1937-2019 Ledrappier, François École d'Été de Probabilités de Saint-Flour XII - 1982 Lecture notes in mathematics Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)1071861417 |
| title | École d'Été de Probabilités de Saint-Flour XII - 1982 |
| title_auth | École d'Été de Probabilités de Saint-Flour XII - 1982 |
| title_exact_search | École d'Été de Probabilités de Saint-Flour XII - 1982 |
| title_full | École d'Été de Probabilités de Saint-Flour XII - 1982 R. M. Dudley ; H. Kunita ; F. Ledrappier. Éd. par P. L. Hennequin |
| title_fullStr | École d'Été de Probabilités de Saint-Flour XII - 1982 R. M. Dudley ; H. Kunita ; F. Ledrappier. Éd. par P. L. Hennequin |
| title_full_unstemmed | École d'Été de Probabilités de Saint-Flour XII - 1982 R. M. Dudley ; H. Kunita ; F. Ledrappier. Éd. par P. L. Hennequin |
| title_short | École d'Été de Probabilités de Saint-Flour XII - 1982 |
| title_sort | ecole d ete de probabilites de saint flour xii 1982 |
| topic | Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Wahrscheinlichkeitsrechnung Konferenzschrift Saint-Flour <1982> |
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