This volume contains lectures given at the Saint-Flour Summer School of Probability Theory during 17th Aug. - 3rd Sept. 1998.
The contents of the three courses are the following:
- Continuous martingales on differential manifolds.
- Topics in non-parametric statistics.
- Free probability theory.
The reader is expected to have a graduate level in probability theory and statistics. This book is of interest to PhD students in probability and statistics or operators theory as well as for researchers in all these fields. The series of lecture notes from the Saint-Flour Probability Summer School can be considered as an encyclopedia of probability theory and related fields.
Author(s): Michel Emery, Arkadi Nemirovski, Dan Voiculescu (auth.), Pierre Bernard (eds.)
Series: Lecture Notes in Mathematics 1738
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2000
Language: English-French
Pages: 349
Tags: Probability Theory and Stochastic Processes; Analysis; Differential Geometry; Statistical Theory and Methods
Introduction....Pages 3-4
Variétés, vecteurs, covecteurs, diffuseurs, codiffuseurs....Pages 5-21
Semimartingales dans une variété et géométrie d’ordre 2....Pages 22-37
Connexions et martingales....Pages 38-51
Fonctions convexes et comportement des martingales....Pages 52-72
Mouvements browniens et applications harmoniques....Pages 73-84
Preface....Pages 88-88
Estimating regression functions from Hölder balls....Pages 89-112
Estimating regression functions from Sobolev balls....Pages 113-131
Spatial adaptive estimation on Sobolev balls....Pages 132-154
Estimating signals satisfying differential inequalities....Pages 155-182
Aggregation of estimates, I....Pages 183-206
Aggregation of estimates, II....Pages 207-227
Estimating functionals, I....Pages 228-257
Estimating functionals, II....Pages 258-277
Introduction....Pages 283-284
Noncommutative probability and operator algebra background....Pages 284-294
Addition of freely independent noncommutative random variables....Pages 294-308
Multiplication of freely independent noncommutative random variables....Pages 308-313
Generalized canonical form, noncrossing partitions....Pages 313-316
Free independence with amalgamation....Pages 316-319
Some basic free processes....Pages 319-325
Random matrices in the large N limit....Pages 325-331
Free entropy....Pages 332-349
