Lectures on Probability Theory & Statistics

by Emery, M.; Nemirovski, A.; Voiculescu, D.; Bernard, Pierre; Dold, A.; Takens, F.; Teissier, B.

• ISBN13: 9783540677369
• ISBN10: 3540677364
• Format: Paperback
• Copyright: 2000-09-01
• Publisher: Springer Verlag

Summary

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.

Table of Contents

"Martingales Continues Dans Les Varietes Differentiables"

Introduction

Variete, vecteurs, covecteurs, diffuseurs, codiffuseurs

Semimartingales dans une variete et geometrie d'ordre 2

Connexions et martingales

Fonctions convexes et comportement des martingales

Mouvements browniens et applications harmoniques

References

"Topics in Non-Parametric Statistics"

Estimating regression functions from Holder balls

Estimating regression functions from Sobolev balls

Spatial adaptive estimation on Sobolev balls

Estimating signals satisfying differential inequalities

Aggregation of estimates, I

Aggregation of estimates, II

Estimating functionals, I

Estimating functionals, II

Bibliography

"Lectures on Free Probability Theory"

Introduction

Noncommutative Probability and Operator Algebra Background

Addition of Freely Independent Noncommutative Random Variables

Multiplication of Freely Independent Noncommutative Random Variables

Generalized Canonical Form, Noncrossing Partitions

Free Independence with Amalgamation

Some Basic Free Processes

Random Matrices in the Large N Limit

Free Entropy

References

List of Tables

Liste of Participants

List of Previous Volumes of the "Ecole d'Ete de Probabilites"

Table of Contents provided by Blackwell. All Rights Reserved.