Probability Essentials

Jean Jacod, Philip Protter

266 pages, parution le 12/11/2002 (2^eme édition)

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Résumé

This introduction to Probability Theory can be used, at the beginning graduate level, for a one-semester course on Probability Theory or for self-direction without benefit of a formal course; the measure theory needed is developed in the text. It will also be useful for students and teachers in related areas such as Finance Theory (Economics), Electrical Engineering, and Operations Research. The text covers the essentials in a directed and lean way with 28 short chapters. Assuming of readers only an undergraduate background in mathematics, it brings them from a starting knowledge of the subject to a knowledge of the basics of Martingale Theory. After learning Probability Theory from this text, the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference. The second edition contains some additions to the text and to the references and some parts are completely rewritten.

Contents

Introduction
Axioms of Probability
Conditional Probability and Independence
Probabilities on a Finite or Countable Space
Random Variables on a Countable Space
Construction of a Probability Measure
Construction of a Probability Measure on R
Random Variables
Integration with Respect to a Probability Measure
Independent Random Variables
Probability Distributions on R
Probability Distributions on Rn
Characteristic Functions
Properties of Characteristic Functions
Sums of Independent Random Variables
Gaussian Random Variables (The Normal and the Multivariate Normal Distributions) Convergence of Random Variables
Weak Convergence
Weak Convergence and Characteristic Functions
The Laws of Large Numbers
The Central Limit Theorem
L2 and Hilbert Spaces
Conditional Expectation
Martingales
Supermartingales and Submartingales
Martingale Inequalities
Martingale Convergence Theorems
The Radon-Nikodym Theorem

L'auteur - Jean Jacod

Universite de Paris VI, Paris, France;

L'auteur - Philip Protter

Cornell University, Ithaca, NY, USA

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Jean Jacod, Philip Protter
Parution	12/11/2002
Édition	2^eme édition
Nb. de pages	266
Format	15,5 x 23,5
Couverture	Broché
Poids	420g
Intérieur	Noir et Blanc
EAN13	9783540438717