A User’s Guide to Measure Theoretic Probability 1st Edition by David Pollard ISBN 0521002893 978-0521002899
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Product details:
ISBN 10: 0521002893
ISBN 13: 978-0521002899
Author: David Pollard
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 independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation 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 what they mean.
Table of contents:
Chapter 1 – Motivation
Chapter 2 – A Modicum of Measure Theory
Chapter 3 – Densities and Derivatives
Chapter 4 – Product Spaces and Independence
Chapter 5 – Conditioning
Chapter 6 – Martingale et al.
Chapter 7 – Convergence in Distribution
Chapter 8 – Fourier Transforms
Chapter 9 – Brownian Motion
Chapter 10 – Representations and Couplings
Chapter 11 – Exponential Tails and the Law of the Iterated Logarithm
Chapter 12 – Multivariate Normal Distributions
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