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Probability and Statistics

Volume II

  • Didier Dacunha-Castelle
  • Marie Duflo

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Didier Dacunha-Castelle, Marie Duflo
    Pages 1-12
  3. Didier Dacunha-Castelle, Marie Duflo
    Pages 13-61
  4. Didier Dacunha-Castelle, Marie Duflo
    Pages 62-114
  5. Didier Dacunha-Castelle, Marie Duflo
    Pages 115-156
  6. Didier Dacunha-Castelle, Marie Duflo
    Pages 157-206
  7. Didier Dacunha-Castelle, Marie Duflo
    Pages 207-248
  8. Didier Dacunha-Castelle, Marie Duflo
    Pages 249-288
  9. Didier Dacunha-Castelle, Marie Duflo
    Pages 289-330
  10. Didier Dacunha-Castelle, Marie Duflo
    Pages 331-388
  11. Back Matter
    Pages 389-409

About this book

Introduction

How can we predict the future without asking an astrologer? When a phenomenon is not evolving, experiments can be repeated and observations therefore accumulated; this is what we have done in Volume I. However history does not repeat itself. Prediction of the future can only be based on the evolution observed in the past. Yet certain phenomena are stable enough so that observation in a sufficient interval of time gives usable information on the future or the mechanism of evolution. Technically, the keys to asymptotic statistics are the following: laws of large numbers, central limit theorems, and likelihood calculations. We have sought the shortest route to these theorems by neglecting to present the most general models. The future statistician will use the foundations of the statistics of processes and should satisfy himself about the unity of the methods employed. At the same time, we have adhered as closely as possible to present day ideas of the theory of processes. For those who wish to follow the study of probabilities to postgraduate level, it is not a waste of time to begin with the least difficult technical situations. This book for final year mathematics courses is not the end of the matter. It acts as a springboard either for dealing concretely with the problems of the statistics of processes, or viii In trod uction to study in depth the more subtle aspects of probabilities.

Keywords

Brownian motion Markov chain Martingal Martingale Poisson process Random Walk counting process estimator likelihood measure theory point process probability statistics stochastic calculus time series

Authors and affiliations

  • Didier Dacunha-Castelle
    • 1
  • Marie Duflo
    • 2
  1. 1.Equipe de Recherche Associée au C.N.R.S. 532 Statistique Appliqué MathématiqueUniversité de Paris-SudOrsay CedexFrance
  2. 2.Université de Paris-NordVilletaneuseFrance

Bibliographic information