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"This book is an introductory text on the beginning graduate level. Its subjects are the measure theoretical foundation of the theory and the main laws and theorems which emerge therefrom. The authors concentrate on certain important topics, primarily independence, interchangeability, and martingales. Particular emphasis is placed on stopping times, as tools in proving theorems as well as objects of interest in themselves. Among their applications is renewal theory; another useful application explained in this book is connected with the limiting behavior of random walks. A knowledge of measure theory is not assumed by the authors who intertwine measure and probability in their presentation as opposed to the customary sharp demarcation. The book can, however, be used as a text for students who have already been exposed to a course in measure theory. Many examples and exercises accompany the text."
"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). An axiomatic mold and measure-theoretic framework for probability theory was furnished by Kolmogorov. In this so-called objective or measure theoretic approach, definitions and axioms are so chosen that the empirical realization of an event is the outcome of a not completely determined physical experiment -an experiment which is at least conceptually capable of indefi nite repetition (this notion is due to von Mises). The concrete or intuitive counterpart of the probability of an event is a long run or limiting frequency of the corresponding outcome."
"Now available in paperback. 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 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 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."@en

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"Electronic books"@en
"Electronic books"

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"Probability theory : Independence, interchangeability, martingales"
"Probability theory indipendence interchangeability martingales"
"Probability theory : independence, interchangeability, martingales"@en
"Probability theory : independence, interchangeability, martingales"
"Probability theory"
"Probability theory independence, interchangeability, martingales"@en
"Probability theory independence, interchangeability, martingales"
"Probability theory : independence interchangeability martingales"
"Probability Theory Independence Interchangeability Martingales"
"Probability Theory Independence, Interchangeability, Martingales"
"Probability theory : independence, interchangeability, Martingales"
"Probability theory. Independence, interchangeability, martingales"

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