Probability Theory: Independence, Interchangeability, Martingales (Springer Texts in Statistics) 3rd Edition by Yuan Shih Chow (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is probably not the first probability book you should read. (You should read Feller’s volume I

⭐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.

⭐Very good book! I love it! Very useful for my research work! Just as what I expected and as it was described!

⭐

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