Probability and Statistics Volume II

Probability and Statistics Volume II / by Didier Dacunha-Castelle, Marie Duflo.

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 evolutio...

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Bibliographic Details
Main Authors: Dacunha-Castelle, Didier (Author), Duflo, Marie (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 1986.
Edition:1st ed. 1986.
Series:Springer eBook Collection.
Subjects:
Probabilities.
Statistics .
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 0 Introduction to Random Processes
  • 0.1. Random Evolution Through Time
  • 0.2. Basic Measure Theory
  • 0.3. Convergence in Distribution
  • 1 Time Series
  • 1.1. Second Order Processes
  • 1.2. Spatial Processes with Orthogonal Increments
  • 1.3. Stationary Second Order Processes
  • 1.4. Time Series Statistics
  • 2 Martingales in Discrete Time
  • 2.1. Some Examples
  • 2.2. Martingales
  • 2.3. Stopping
  • 2.4. Convergence of a Submartingale
  • 2.5. Likelihoods
  • 2.6. Square Intergrable Martingales
  • 2.7. Almost Sure Asymptotic Properties
  • 2.8. Central Limit Theorems
  • 3 Asymptotic Statistics
  • 3.1. Models Dominated at Each Instant
  • 3.2. Contrasts
  • 3.3. Rate of Convergence of an Estimator
  • 3.4. Asymptotic Properties of Tests
  • 4 Markov Chains
  • 4.1. Introduction and First Tools
  • 4.2. Recurrent or Transient States
  • 4.3. The Study of a Markov Chain Having a Recurrent State
  • 4.4. Statistics of Markov Chains
  • 5 Step by Step Decisions
  • 5.1. Optimal Stopping
  • 5.2. Control of Markov Chains
  • 5.3. Sequential Statistics
  • 5.4. Large Deviations and Likelihood Tests
  • 6 Counting Processes
  • 6.1. Renewal Processes and Random Walks
  • 6.2. Counting Processes
  • 6.3. Poisson Processes
  • 6.4. Statistics of Counting Processes
  • 7 Processes in Continuous Time
  • 7.1. Stopping Times
  • 7.2. Martingales in Continuous Time
  • 7.3. Processes with Continuous Trajectories
  • 7.4. Functional Central Limit Theorems
  • 8 Stochastic Integrals
  • 8.1. Stochastic Integral with Respect to a Square Integrable Martingale
  • 8.2. Ito’s Formula and Stochastic Calculus
  • 8.3. Asymptotic Study of Point Processes
  • 8.4. Brownian Motion
  • 8.5. Regression and Diffusions
  • Notations and Conventions.

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