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A User's Guide to Measure Theoretic Probability / Edition 1

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Overview

This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independendence, conditioning, martingales , convergence in distribution, and Fourier transforms. In addition the re are numerous sections treating topics traditionally thought of as m ore advanced, such as coupling and the KMT strong approximation, optio n pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentatio n of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand wh at they mean.

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Editorial Reviews

From the Publisher
"Unlike technical books of a previous generation, here we have an author admitting that a reader might find the subject difficult and even offering a window on the pedagogical considerations by which he shapes his exposition. Pollard does not just explain and clarify abstractions; he really sells them to a presumably skeptical reader. Thus he bridges a gap in the literature, between elementary probability texts and advanced works that presume a secure prior knowledge of measure theory...The nice layout and occasional useful diagram further amplify the friendliness of this book." Choice

"The book ... can be recommended as an excellent source in measuring theoretic probability theory as well as a handbook for everybody who studies stochastic processes in the real world." Mathematical Reviews

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Product Details

Table of Contents

Preface
Ch. 1 Motivation
Ch. 2 A modicum of measure theory
Ch. 3 Densities and derivatives
Ch. 4 Product spaces and independence
Ch. 5 Conditioning
Ch. 6 Martingale et al.
Ch. 7 Convergence in distribution
Ch. 8 Fourier transforms
Ch. 9 Brownian motion
Ch. 10 Representations and couplings
Ch. 11 Exponential tails and the law of the iterated logarithm
Ch. 12 Multivariate normal distributions
App. A Measures and integrals
App. B Hilbert spaces
App. C Convexity
App. D Binomial and normal distributions
App. E Martingales in continuous time
App. F Disintegration of measures
Index
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