Lectures on probability theory and statistics:
Saved in:
| Format: | Conference Proceeding Book |
|---|---|
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London
Springer
2000
|
| Series: | Lecture notes in mathematics
1738 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | In franz. und engl. Sprache |
| Physical Description: | XI, 349 S. Ill., graph. Darst. |
| ISBN: | 3540677364 |
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| 245 | 1 | 0 | |a Lectures on probability theory and statistics |c Ecole d'Eté de Probabilités de Saint-Flour XXVIII - 1998. M. Emery ; A. Nemirovski ; D. Voiculescu. Ed.: Pierre Bernard |
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London |b Springer |c 2000 | |
| 300 | |a XI, 349 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1738 | |
| 500 | |a In franz. und engl. Sprache | ||
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Record in the Search Index
| _version_ | 1804127965319004160 |
|---|---|
| adam_text | TABLE
OF
CONTENTS
Michel
EMERY
:
MARTINGALES CONTINUES DANS
LES VARIETES DIFFERENTIABLES
Introduction
1.
Variété, vecteurs, covecteurs, diffuseurs, codiffuseurs
1.
Variétés, sous variétés, applications CP
5
2.
Vecteurs et covecteurs tangents
8
3.
Diffuseurs
12
4.
Codiffuseurs
15
2.
Semimartingales dans une variété et géométrie d ordre
2
1.
Brefs rappels sur les semimartingales continues
22
2.
Semimartingales dans une variété
25
3.
Intégration des codiffuseurs le long des semimartingales
28
4.
Intégrales de Stratonovitch
32
5.
Topologie
des semimartingales dans une variété
34
3.
Connexions et martingales
1.
Connexions et géodésiques
38
2.
Intégrales d Itô et martingales
43
3.
Applications affines
;
connexion produit
48
4.
Fonctions convexes et comportement des martingales
1.
Fonctions convexes et convergence à l infini des martingales
52
2.
Caractérisation des martingales par les fonctions convexes
55
3.
Détermination des martingales par leurs valeurs finales
61
5.
Mouvements browniens et applications harmoniques
1.
Variétés riemaniennes et mouvements browniens
73
2.
Applications harmoniques
76
Références
80
VIII
Arkadi
NEMÍRO
VSR!
:
TOPICS in NON-PARAMETRIC
STATISTICS
1.
Estimating regression functions from Holder balls
1.1
Introduction
1.2
Recovering a univariate Lipschitz continuous function
1.3
Extension
:
recovering functions from Holder balls
1.4
Appendix
:
proof of the
Fano
inequality
2.
Estimating regression functions from Sobolev balls
2.1
Lower bounds for the minimax risk
2.2
Upper bounds on the minimax risk
2.3
Appendix
:
Proofs of the Theorems
2.1.1,2.1.2
3
Spatial adaptive estimation on Sobolev balls
3.1
Spatial adaptive estimation
:
the goal
3.2
The estimate
3.3
Quality of estimation
3.4
Optimality index of the adaptive estimate
4
Estimating signals satisfying differential inequalities
4.1
The goal
4.2
Estimating solutions of homogeneous equations
4.2.1
Preliminaries
4.2.2
Estimating sequences
4.2.3
Discussion
4.3
From sequences to functions
4.3.1
Spatial adaptive estimate
:
preliminaries
4.3.2
Spatial adaptive estimate
:
construction and quality
4.3.3
Frequency modulated signals
4.4
Appendix
:
Proofs of Lemmas
4.2.1, 4.3.1
4.4.1
Proof of Lemma
4.2.1
4.4.2
Proof of Lemma
4.3.1
5
Aggregation of estimates, I
5.1
Motivation
5.2
The problem and the main result
5.2.1
Aggregation problem
5.2.2
The recovering routine
5.2.3
Main result
5.2.4
Concentration
5.3
Lower bound
5.4
Application
:
Recovering functions from
Barrons
class
5.5
Numerical example
:
nonparametric filtration
IX
6
Aggregation of estimates, II
6.1
Gaussian white noise model of observations
207
6.2
Approximating the best linear combination of estimates
210
6.3
Application
:
aggregating projection estimates
215
6.3.1
Linear estimates
215
6.3.2
Aggregating projection estimates
218
6.3.3
The construction
219
6.4
Approximating the best of given estimates
225
7
Estimating functionals, I
7.1
The problem
228
7.1.1
Lower bounds and asymptotical efficiency
229
7.2
The case of once continuously differentiable functional
234
7.2.1
Whether condition
(7.2.2)
is sharp
? 240
7.3
Increasing smoothness of
F
246
7.3.1
The case of twice continuously differentiable functional
247
7.3.2
Concluding remarks
256
8
Estimating functionals, II
8.1
Preliminaries
:
estimating polynomials
258
8.1.1
Hilbert-Schmidt polynomials
259
8.1.2
Estimating Hilbert-Schmidt polynomials
260
8.1.3
Extension
264
8.2
From polynomials to smooth functionals
265
8.2.1
Measure concentration
267
8.2.2
The estimate
269
Bibliography
275
DAN VOICULESCU
:
LECTURES ON FREE PROBABILITY
THEORY
0
Introduction
283
1.
Noncommutative
Probability and Operator
Algebra Background
1.1
Noncommutative
probability spaces
284
1.2
C*-probability spaces
284
1.3
W*-probability spaces
285
1.4
Examples
285
1.5
The distributions of
noncommutative
random variables
286
1.6
Examples
287
1.7
Usual independence
288
1.8
Free independence
288
1.9
Examples
290
1.10
Further properties of free independence
291
1.11
Free products
293
2. Addition
of Freely Independent
Noncommutative
Random Variables
2.1
Additive free convolution
2.2
Canonical form
2.3
Compactly suported probability measures on
91
2.4
The fi-transform
2.5
The free central limit theorem
2.6
Superconvergence
in the free central limit theorem
2.7
The free
Poisson
law
2.8
The relation of free
Poisson
to be semicircle
2.9
Free convolution of measures with unbounded support
2.10
The Cauchy distribution
2.11
Free infinite divisibility and the free analogue of the Levy-Hincin theorem
2.12
Free stable laws
2.13
More free harmonic analysis on
91
2.14
Spectra of convolution operators on free products of groups
3
Multiplication of Freely Independent
Noncommutative
Random Variables
3.1
Multiplicative free convolution
3.2
Probability measures on
9Î
>
OandT
3.3
The S-fransform
3.4
Examples
3.5
Multiplicative free infinite divisibility on
Τ
3.6
Multiplicative free infinite divisibility on
9Í
> 0
4
Generalized Canonical Form, Noncrossing Partitions
4.1
Combinatorial work
4.2
Generalized canonical form
4.3
Noncrossing partitions and the formula for
θ
5
Free Independence with Amalgamation
5.1
Classical background on conditional independence
5.2
Conditional expectations in
von
Neumann algebras
with trace state (background)
5.3
Noncommutative
probability spaces over
В
and free
independence over
В
5.4
More on B-free probability theory
Some Basic Free Processes
6.1
The semicircular functor (free analogue of the Gaussian functor)
6.2
Free
Poisson
processes
6.3
Stationary processes with free increments
6.4
The Markov transitions property of processes with free increments
6.5
Free Markovianity
6.6
Further results
XI
7
Random Matrices in the Large
Л
Limit
7.1
Asymptotic free independence for Gaussian matrices
325
7.2
Asymptotic free independence for unitary matrices
328
7.3
Corollaries of the basic asymptotic free independence results
329
7.4
Further asymptotic free independence results
331
8
Free Entropy
8.1
Clarifications
332
8.2
Background on classical entropy via microstates
332
8.3
Free entropy via
matricial
microstates
333
8.4
Properties of
χ (Χι,-, Χη)
334
8.5
Free entropy dimension
338
8.6
Classical Fisher information and the adjoint of the derivation
339
8.7
Free Fisher information of one variable
340
8.8
The underlying idea of the microstates-free-approach
341
8.9
Noncommutative
Hubert transforms
341
8.10
Free Fisher information and free entropy in the
344
microstate-free approach
9
References
346
List of Tables
350
Liste
of Participants
352
List of Previous Volumes of the
„Ecole d Eté de Probabilités
353
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:41:43Z |
| institution | BVB |
| institution_GND | (DE-588)2183999-2 |
| isbn | 3540677364 |
| language | English |
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| physical | XI, 349 S. Ill., graph. Darst. |
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| spelling | Lectures on probability theory and statistics Ecole d'Eté de Probabilités de Saint-Flour XXVIII - 1998. M. Emery ; A. Nemirovski ; D. Voiculescu. Ed.: Pierre Bernard Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London Springer 2000 XI, 349 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1738 In franz. und engl. Sprache Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1998 Saint-Flour gnd-content Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Statistik (DE-588)4056995-0 s DE-604 Émery, Michel 1949- Sonstige (DE-588)111816637 oth Nemirovskij, Arkadij S. 1947- Sonstige (DE-588)12209395X oth Voiculescu, Dan 1949- Sonstige (DE-588)122093968 oth Bernard, Pierre Sonstige oth Ecole d'Eté de Probabilités 28 1998 Saint-Flour Sonstige (DE-588)2183999-2 oth Lecture notes in mathematics 1738 (DE-604)BV000676446 1738 Digitalisierung TU Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009000758&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lectures on probability theory and statistics Lecture notes in mathematics Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4056995-0 (DE-588)1071861417 |
| title | Lectures on probability theory and statistics |
| title_auth | Lectures on probability theory and statistics |
| title_exact_search | Lectures on probability theory and statistics |
| title_full | Lectures on probability theory and statistics Ecole d'Eté de Probabilités de Saint-Flour XXVIII - 1998. M. Emery ; A. Nemirovski ; D. Voiculescu. Ed.: Pierre Bernard |
| title_fullStr | Lectures on probability theory and statistics Ecole d'Eté de Probabilités de Saint-Flour XXVIII - 1998. M. Emery ; A. Nemirovski ; D. Voiculescu. Ed.: Pierre Bernard |
| title_full_unstemmed | Lectures on probability theory and statistics Ecole d'Eté de Probabilités de Saint-Flour XXVIII - 1998. M. Emery ; A. Nemirovski ; D. Voiculescu. Ed.: Pierre Bernard |
| title_short | Lectures on probability theory and statistics |
| title_sort | lectures on probability theory and statistics |
| topic | Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Wahrscheinlichkeitstheorie Statistik Konferenzschrift 1998 Saint-Flour |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009000758&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT emerymichel lecturesonprobabilitytheoryandstatistics AT nemirovskijarkadijs lecturesonprobabilitytheoryandstatistics AT voiculescudan lecturesonprobabilitytheoryandstatistics AT bernardpierre lecturesonprobabilitytheoryandstatistics AT ecoledetedeprobabilitessaintflour lecturesonprobabilitytheoryandstatistics |