Probability Theory: Independence, Interchangeability, Martingales

Chow, Yuan Shih; Teicher, Henry

ISBN 10: 1461219515 / ISBN 13: 9781461219514

Published by Springer, 2021

About this Item

Seller Inventory # 26400824222

Bibliographic Details

• Title: Probability Theory: Independence, Interchangeability, Martingales
• Publisher: Springer
• Publication Date: 2021
• Language: English
• ISBN 10: 1461219515
• ISBN 13: 9781461219514
• Binding: Soft cover
• Condition: New

About this title

Synopsis

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.