Probability Theory

Independence, Interchangeability, Martingales

Yuan Shih Chow, Henry Teicher

490 pages, parution le 24/11/2003

Ajouter à une liste

Indisponible

Résumé

Comprising the major theorems of probability theory and the measure theoretical foundations of the subject, the main topics treated here are independence, interchangeability, and martingales. Particular emphasis is placed upon stopping times, both as tools in proving theorems and as objects of interest themselves. No prior knowledge of measure theory is assumed and a unique feature of the book is the combined presentation of measure and probability. It is easily adapted for graduate students familiar with measure theory using the guidelines given.

Special features include:

A comprehensive treatment of the law of the iterated logarithm
The Marcinklewicz-Zygmund inequality, its extension to martingales and applications thereof
Development and applications of the second moment analogue of Walds equation
Limit theorems for martingale arrays; the central limit theorem for the interchangeable and martingale cases; moment convergence in the central limit theorem
Complete discussion, including central limit theorem, of the random casting of r balls into n cells
Recent martingale inequalities
Cram r-L vy theorem and factor-closed families of distributions.

Written for:
Graduate students, researchers

Classes of Sets, Measures,and Probability Spaces
Binomial Random Variables
Independence
Integration in a Probability Space
Sums of Independent Random Variables
Measure Extensions, Lebesgue-Stieltjes Measure, Kolmogorov Consistency Theorem
Conditional Expectation, Conditional Independence, Introduction to Martingales
Distribution Functions and Characteristic Functions
Central Limit Theorems
Limit Theorems for Independent Random Variables
Martingales
Infinitely Divisible Laws
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Yuan Shih Chow, Henry Teicher
Parution	24/11/2003
Nb. de pages	490
Format	15,5 x 23,5
Couverture	Broché
Poids	715g
Intérieur	Noir et Blanc
EAN13	9780387406077
ISBN13	978-0-387-40607-7