[I943.Ebook] PDF Download Probability Theory: Independence, Interchangeability, Martingales (Springer Texts Statistics), by Yuan Shih Chow, Henry Teicher
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Probability Theory: Independence, Interchangeability, Martingales (Springer Texts Statistics), by Yuan Shih Chow, Henry Teicher
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Apart from new examples and exercises, some simplifications of proofs, minor improvements, and correction of typographical errors, the principal change from the first edition is the addition of section 9.5, dealing with the central limit theorem for martingales and more general stochastic arrays. vii Preface to the First Edition Probability theory is a branch of mathematics dealing with chance phenomena and has clearly discernible links with the real world. The origins of the sub ject, generally attributed to investigations by the renowned French mathe matician Fermat of problems posed by a gambling contemporary to Pascal, have been pushed back a century earlier to the Italian mathematicians Cardano and Tartaglia about 1570 (Ore, 1953). Results as significant as the Bernoulli weak law of large numbers appeared as early as 1713, although its counterpart, the Borel strong law oflarge numbers, did not emerge until 1909. Central limit theorems and conditional probabilities were already being investigated in the eighteenth century, but the first serious attempts to grapple with the logical foundations of probability seem to be Keynes (1921), von Mises (1928; 1931), and Kolmogorov (1933).
- Sales Rank: #4643081 in Books
- Published on: 1988-09
- Original language: English
- Number of items: 1
- Dimensions: 9.50" h x 6.25" w x 1.25" l,
- Binding: Hardcover
Most helpful customer reviews
3 of 4 people found the following review helpful.
Second Course on Probability
By Abstract Space
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.
4 of 10 people found the following review helpful.
a difficult book
By A Customer
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.
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