Mathematics of probability
著者
書誌事項
Mathematics of probability
（Graduate studies in mathematics, v. 149）
American Mathematical Society, c2013
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注記
Includes bibliographical references (p. 279) and index
内容説明・目次
内容説明
This book covers the basics of modern probability theory. It begins with probability theory on finite and countable sample spaces and then passes from there to a concise course on measure theory, which is followed by some initial applications to probability theory, including independence and conditional expectations. The second half of the book deals with Gaussian random variables, with Markov chains, with a few continuous parameter processes, including Brownian motion, and, finally, with martingales, both discrete and continuous parameter ones. The book is a self-contained introduction to probability theory and the measure theory required to study it.
目次
Preface
Some background and preliminaries
Probability theory on uncountable sample spaces
Some applications to probability theory
The central limit theorem and Gaussian distributions
Discrete parameter stochastic processes
Some continuous-time processes
Martingales
Notation
Bibliography
Index
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