Probability Theory: Independence, Interchangeability, Martingales by Henry Teich

Description: Probability Theory by Henry Teicher, Yuan Shih Chow 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; FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher 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 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 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 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. Notes This is a classic 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. Author Biography Teicher-Rutgers University, New Brunswick, NJ Table of Contents 1 Classes of Sets, Measures, and Probability Spaces.- 1.1 Sets and set operations.- 1.2 Spaces and indicators.- 1.3 Sigma-algebras, measurable spaces, and product spaces.- 1.4 Measurable transformations.- 1.5 Additive set functions, measures, and probability spaces.- 1.6 Induced measures and distribution functions.- 2 Binomial Random Variables.- 2.1 Poisson theorem, interchangeable events, and their limiting probabilities.- 2.2 Bernoulli, Borel theorems.- 2.3 Central limit theorem for binomial random variables, large deviations.- 3 Independence.- 3.1 Independence, random allocation of balls into cells.- 3.2 Borel-Cantelli theorem, characterization of independence, Kolmogorov zero-one law.- 3.3 Convergence in probability, almost certain convergence, and their equivalence for sums of independent random variables.- 3.4 Bernoulli trials.- 4 Integration in a Probability Space.- 4.1 Definition, properties of the integral, monotone convergence theorem.- 4.2 Indefinite integrals, uniform integrability, mean convergence.- 4.3 Jensen, Hölder, Schwarz inequalities.- 5 Sums of Independent Random Variables.- 5.1 Three series theorem.- 5.2 Laws of large numbers.- 5.3 Stopping times, copies of stopping times, Walds equation.- 5.4 Chung—Fuchs theorem, elementary renewal theorem, optimal stopping.- 6 Measure Extensions, Lebesgue—Stieltjes Measure,Kolmogorov Consistency Theorem.- 6.1 Measure extensions, Lebesgue—Stieltjes measure 165 6.2 Integration in a measure space.- 6.3 Product measure, Fubinis theorem, n-dimensional Lebesgue—Stieltjes measure.- 6.4 Infinite-dimensional product measure space, Kolmogorov consistency theorem.- 6.5 Absolute continuity of measures, distribution functions; Radon—Nikodym theorem.- 7 Conditional Expectation, Conditional Independence,Introduction to Martingales.- 7.1 Conditional expectations.- 7.2 Conditional probabilities, conditional probability measures.- 7.3 Conditional independence, interchangeable random variables.- 7.4 Introduction to martingales.- 7.5 U-statistics.- 8 Distribution Functions and Characteristic Functions.- 8.1 Convergence of distribution functions, uniform integrability, Helly—Bray theorem.- 8.2 Weak compactness, Fréchet—Shohat, GlivenkoCantelli theorems.- 8.3 Characteristic functions, inversion formula, Lévy continuity theorem.- 8.4 The nature of characteristic functions, analytic characteristic functions, Cramér—Lévy theorem.- 8.5 Remarks on k-dimensional distribution functions and characteristic functions.- 9 Central Limit Theorems.- 9.1 Independent components.- 9.2 Interchangeable components.- 9.3 The martingale case.- 9.4 Miscellaneous central limit theorems.- 9.5 Central limit theorems for double arrays.- 10 Limit Theorems for Independent Random Variables.- 10.1 Laws of large numbers.- 10.2 Law of the iterated logarithm.- 10.3 Marcinkiewicz—Zygmund inequality, dominated ergodic theorems.- 10.4 Maxima of random walks.- 11 Martingales.- 11.1 Uperossing inequality and convergence.- 11.2 Martingale extension of Marcinkiewicz-Zygmund inequalities.- 11.3 Convex function inequalities for martingales.- 11.4 Stochastic inequalities.- 12 Infinitely Divisible Laws.- 12.1 Infinitely divisible characteristic functions.- 12.2 Infinitely divisible laws as limits.- 12.3 Stable laws. Long 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 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 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 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. Feature A classic book, now in its third edition, is an essential reference to researchers and graduate students in probability theory The new edition contains much new material, including U-statistic, additional theorems and examples, as well as simpler versions of some proofs Description for Sales People This is a classic 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. Details ISBN0387406077 Author Yuan Shih Chow Series Springer Texts in Statistics Language English Edition 3rd ISBN-10 0387406077 ISBN-13 9780387406077 Media Book Format Paperback Imprint Springer-Verlag New York Inc. Subtitle Independence, Interchangeability, Martingales Place of Publication New York, NY Country of Publication United States DEWEY 519.2 Residence New Brunswick, US Pages 489 Short Title PROBABILITY THEORY 1997/E 3/E Illustrations 1 Illustrations, black and white; XXII, 489 p. 1 illus. DOI 10.1007/b13033;10.1007/978-1-4612-1950-7 AU Release Date 2003-10-17 NZ Release Date 2003-10-17 US Release Date 2003-10-17 UK Release Date 2003-10-17 Publisher Springer-Verlag New York Inc. Edition Description 3rd ed. 1997 Year 2003 Publication Date 2003-10-17 Alternative 9780387982281 Audience General We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96258699;

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