A User's Guide to Measure Theoretic Probability
2001
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Rigorous probabilistic arguments, built on the foundation of measure theory introduced eighty years ago by Kolmogorov, have invaded many fields. Students of statistics, biostatistics, econometrics, finance, and other changing disciplines now find themselves needing to absorb theory beyond what they might have learned in the typical undergraduate, calculus-based probability course. This 2002 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.
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Author
David Pollard
Author · 1 books
David Pollard was born in London in 1942. He fled accountancy to the University of Sussex where he was given his three degrees in literature, the history of ideas and philosophy. The last of these, a doctorate, was published as The Poetry of Keats: Language and Experience and is a Heideggerian interpretation of the poet. He has also published other work on Keats, as well as on Blake and Nietzsche. His latest, Nietzsche’s Footfalls, a meditation on the philosopher and his times, came out in 2003. He has also reviewed extensively in the fields of both philosophy and literature. Pollard’s work has appeared in: Omphalos, Tears in the Fence, Aletheia, Fire, Eratica, Eclipse and Poetry Monthly. He is curently writing a comparison of Blake and Nietzsche.
