Probability Theory: Independence, Interchangeability, Martingales (Springer Texts in Statistics)

• Publisher:   Springer
• Number Of Pages:   488
• Publication Date:   1997-09-11
• ISBN-10 / ASIN:   0387982280
• ISBN-13 / EAN:   9780387982281

This is a text comprising the major theorems of probability theory and the measure theoretical foundations of the subject. The main topics treated 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 familar with measure theory as indicated by the guidelines in the preface. 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 Wald's equation . Limit theorems for martingale arrays; the central limit theorem for the interchangeable and martingale cases; moment convergence i! n 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 theore and factor-closed families of distributions This edition includes a section dealing with U-statistic, adds additional theorems and examples, and includes simpler versions of some proofs.

This book is probably not the first probability book you should read. (You should read Feller's volume I An Introduction to Probability Theory and Its Applications, Volume 1 for the initiation). However, if you like rigor and modern treatment of probability theory, this is for you. It provides a comprehensice treatment of many modern topics in probability which are necessary for many statistical problems. There are beautiful and elegant coverages on independence, exchangeble variables, martingales, U-statistics, and limit theorems. There may be other topics which you have to find from other books, if you use this book as a second probability text. You need to add topics on stochastic processes, such as Markov process and Markov chains, branching process, renewal process, point process, stationary process (both strict sense and wide sense). Of course, these topics may likely to be taught in another separate course on stochastic process. I think the purpose of theoretical probability training is to allow students to use probability tools to understand and develop common statistical theory such as asymptotic statistics and distributional approximations. Probability is also used to model many real-world phenomena and that's another field called Applied Probability, which should be interesting topics for application-oriented students and students from other fields, and should be taught in the first course on probability.

This book has been referred by many mathematical economists and I think this book is one of the most excellent books in this field. But this book is written very rigorously and is very difficult to follow. Oh, don't get me wrong! I'm convinced this book will serve the bridge between an elementary level and a more high level.

password: gigapedia

rapidshare.com download (Report broken link)

Bookmark Probability Theory: Independence, Interchangeability, Martingales (Springer Texts in Statistics)

Hyperlink code: