Probability Theory, an Analytic View

Rating:
Summary: An excellent reference
Review: I am using this book as a reference for a first graduate coursein Probability Theory. In all fairness I must confess that I have notread the whole book, though I have browsed through it and I have read a few pieces here and there. My reason for selecting this book as a reference is partly the fact that the instructor is not using a book, only his notes and this book is listed as an additional reference. Having done some serious book browsing before settling on this one, I can say that its certainly more advanced than typical "first graduate course" books like the ones by Durrett or Williams. The author assumes knowledge of real analysis and launches right away into Probability. The book covers topics like convergence of probability measures and Wiener measure which are given little or no mention in Durrett's and Williams' books. The author in fact devotes an entire chapter to Wiener measure. I don't know if I would like to use this book in isolation. Its pretty advanced and has a whole lot of material that'll take a very long time to read, at least for me. On the other hand, Stroock is a star in the field of Probability and I like his style of writing which is why I did not hesitate to invest a small amount of money (by textbook standards) on an obviously excellent, but difficult reference.

Rating:
Summary: probability via analysis and Stein's Method
Review: Stroock in the preface to his preface gives his graduate school introduction to probability from Kac and McKean to explain why the book is written from the analytic rather than the probabilistic viewpoint. The coverage is thorough and rigorous with important proofs provided in the style he likes best. As an example in Chapter 2 where he covers the central limit theorem and the Berry-Esseen results on rates of convergence, he uses Stein's method rather than more complicated approaches using Fourier series.

This covers all the standard topics for a first year graduate course in probability and a bit more.