Probability Theory Independence, Interchangeability, Martingales

ISBN-10: 0387406077
ISBN-13: 9780387406077
Edition: 3rd 1997 (Revised)
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Description: 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  More...

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Book details

List price: $69.95
Edition: 3rd
Copyright year: 1997
Publisher: Springer
Publication date: 10/17/2003
Binding: Paperback
Pages: 489
Size: 6.50" wide x 8.75" long x 1.00" tall
Weight: 1.584
Language: English

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:nbsp;A comprehensive treatment of the law of the iterated logarithm;nbsp;the Marcinklewicz-Zygmund inequality, its extension to martingales and applications thereof;nbsp;nbsp;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.

Classes of Sets, Measures,and Probability Spaces
Binomial Random Variables
Independence
Integration in a Probability Space
Sums of Independent Random Variables
Measure Extensions, Lebesgue-Stieltjes Measure, Kolmogorov Consistency Theorem
Conditional Expectation, Conditional Independence, Introduction to Martingales
Distribution Functions and Characteristic Functions
Central Limit Theorems
Limit Theorems for Independent Random Variables
Martingales
Infinitely Divisible Laws
Index

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