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Lectures on Probability Theory and Statistics

Ecole d'Ete de Probabilites de Saint-Flour XXVIII - 1998

  • Book
  • © 2000

Overview

Authors:
  1. Michel Emery
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  2. Arkadi Nemirovski
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  3. Dan Voiculescu
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Editors:
  1. Pierre Bernard
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1738)

Part of the book sub series: École d'Été de Probabilités de Saint-Flour (LNMECOLE)

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Table of contents (24 chapters)

  1. Front Matter

    Pages I-XIII
    Download chapter PDF

  2. Introduction

    • Michel Emery
    Pages 3-4

  3. Variétés, vecteurs, covecteurs, diffuseurs, codiffuseurs

    • Michel Emery
    Pages 5-21

  4. Semimartingales dans une variété et géométrie d’ordre 2

    • Michel Emery
    Pages 22-37

  5. Connexions et martingales

    • Michel Emery
    Pages 38-51

  6. Fonctions convexes et comportement des martingales

    • Michel Emery, Arkadi Nemirovski, Dan Voiculescu
    Pages 52-72

  7. Mouvements browniens et applications harmoniques

    • Michel Emery, Arkadi Nemirovski, Dan Voiculescu
    Pages 73-84

  8. Preface

    • Arkadi Nemirovski
    Pages 88-88

  9. Estimating regression functions from Hölder balls

    • Arkadi Nemirovski
    Pages 89-112

  10. Estimating regression functions from Sobolev balls

    • Arkadi Nemirovski
    Pages 113-131

  11. Spatial adaptive estimation on Sobolev balls

    • Arkadi Nemirovski
    Pages 132-154

  12. Estimating signals satisfying differential inequalities

    • Arkadi Nemirovski
    Pages 155-182

  13. Aggregation of estimates, I

    • Arkadi Nemirovski
    Pages 183-206

  14. Aggregation of estimates, II

    • Arkadi Nemirovski
    Pages 207-227

  15. Estimating functionals, I

    • Arkadi Nemirovski
    Pages 228-257

  16. Estimating functionals, II

    • Arkadi Nemirovski
    Pages 258-277

  17. Introduction

    • Dan Voiculescu
    Pages 283-284

  18. Noncommutative probability and operator algebra background

    • Dan Voiculescu
    Pages 284-294

  19. Addition of freely independent noncommutative random variables

    • Dan Voiculescu
    Pages 294-308

  20. Multiplication of freely independent noncommutative random variables

    • Dan Voiculescu
    Pages 308-313
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Lectures on Probability Theory and Statistics

  • Book Subtitle: Ecole d'Ete de Probabilites de Saint-Flour XXVIII - 1998

  • Authors: Michel Emery, Arkadi Nemirovski, Dan Voiculescu

  • Editors: Pierre Bernard

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0106703

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag GmbH Germany, part of Springer Nature 2000

  • Softcover ISBN: 978-3-540-67736-9Published: 26 June 2000

  • eBook ISBN: 978-3-540-45029-0Published: 06 May 2007

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIII, 349

  • Topics: Probability Theory and Stochastic Processes, Analysis, Differential Geometry, Statistical Theory and Methods

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