This revised edition of Daniel W. Stroock's classic text is suitable for a first-year graduate course on probability theory. By modern standards the topics treated are classical and the techniques used far-ranging: Dr. Stroock does not approach the subject as a monolithic structure resting on a few basic principles. The first part of the book deals with independent random variables, Central Limit phenomena, the general theory of weak convergence and several of its applications, as well as elements of both the Gaussian and Markovian theory of measures on function space. Stroock covers conditional expectation values in the second half where he applies them to the study of martingales. He also explores the connection between martingales and various aspects of classical analysis and the connections between Wiener's measure and classical potential theory. Student prerequisites are a good grasp of introductory, undergraduate probability theory and a reasonably sophisticated knowledge of analysis.
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Book Description
Editorial Reviews
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"...uniformly well written and well spiced with comments to aid the intuition, so the readership should include a wide range, both of students and of professional probabilists.... We can expect it to take its place alongside the classics of probability theory." Mathematical Reviews
Book Description
This revised edition of Daniel W. Stroock's text is suitable for a first-year graduate course on probability theory. It is intended for students with a good grasp of undergraduate probability and a reasonably sophisticated introduction to modern analysis who now want to learn what these two topics have to say about each other. By modern standards the topics treated here are classical and the techniques used far-ranging. No attempt has been made to present the subject as a monolithic structure resting on a few basic principles. Although primarily intended for students and practitioners of probability theory and analysis, it will also be a valuable reference for those in fields as diverse as physics, engineering, and economics.
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23 of 23 people found the following review helpful:
5.0 out of 5 stars
basic probability but with a Stein twist,an analytical approach,
By
This review is from: Probability Theory, an Analytic View (Paperback)
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.
24 of 26 people found the following review helpful:
5.0 out of 5 stars
An excellent reference,
By chetan (Champaign, IL, USA) - See all my reviews
This review is from: Probability Theory, an Analytic View (Paperback)
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.
12 of 15 people found the following review helpful:
5.0 out of 5 stars
You may have to soak this book up slowly,
By
This review is from: Probability Theory, an Analytic View (Paperback)
I've read some parts of this book and not others,so I suppose I need to reserve the right to revise this opinion from time to time. Many good things in probability theory are not in this book. That is not a fault of this book; it only means you'll need others as well. It has an extremely notation-intensive style, and at first I thought that could slow down the reading a lot. But with the help of the notation table on pages 525 - 528 it actually moves along rather smoothly. If you just wanted to read through a section, carefully checking and understanding the correctness of everything, it wouldn't be that hard, but you'd be wasting the book. You have to go over things until you understand Stroock's point of view---the aspects of it that he's not very explicit about. Maybe it's a bit like learning a language; you have to soak it up and integrate it.
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Inside This Book
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First Sentence:
In one way or another, most probabilistic analysis entails the study of large families of random variables. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nonnegative harmonic function, first entrance time, reversed submartingale, nonnegative martingale, nonnegative submartingale, independent increment process, bounded harmonic function, continuous martingale, natural projection map, whose characteristic function, strong topology, uniform topology, first exit time, nondecreasing sequence, martingale convergence theorem, measurable space, probability generating function, iterated logarithm, harmonic measure, probability space, strong maximum principle, classical potential theory, nonempty open set, totally bounded, lower semicontinuous Key Phrases - Capitalized Phrases (CAPs): (learn more)
Strong Law, Monotone Convergence Theorem, Lebesgue's Dominated Convergence Theorem, Borel-Cantelli Lemma, Fubini's Theorem, Fatou's Lemma, Tonelli's Theorem, Doob's Stopping Time Theorem, E-measurable P-null, Continuity Theorem, Harnack's Principle, Doob's Martingale Convergence Theorem, Theory of Prob, Bochner's Theorem, Dini's Lemma, Hardy's Inequality New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In one way or another, most probabilistic analysis entails the study of large families of random variables. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nonnegative harmonic function, first entrance time, reversed submartingale, nonnegative martingale, nonnegative submartingale, independent increment process, bounded harmonic function, continuous martingale, natural projection map, whose characteristic function, strong topology, uniform topology, first exit time, nondecreasing sequence, martingale convergence theorem, measurable space, probability generating function, iterated logarithm, harmonic measure, probability space, strong maximum principle, classical potential theory, nonempty open set, totally bounded, lower semicontinuous Key Phrases - Capitalized Phrases (CAPs): (learn more)
Strong Law, Monotone Convergence Theorem, Lebesgue's Dominated Convergence Theorem, Borel-Cantelli Lemma, Fubini's Theorem, Fatou's Lemma, Tonelli's Theorem, Doob's Stopping Time Theorem, E-measurable P-null, Continuity Theorem, Harnack's Principle, Doob's Martingale Convergence Theorem, Theory of Prob, Bochner's Theorem, Dini's Lemma, Hardy's Inequality New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 8
books:
See all 8 books this book cites
15
books
cite this book:
See all 15 books citing this book
- Stochastic Processes (Wiley Classics Library) by J. L. Doob on page 285, and page 377
- Real Analysis and Probability (Cambridge Studies in Advanced Mathematics) by R. M. Dudley in Front Matter
- Functional Analysis (Dover Books on Mathematics) by Frigyes Riesz on page 435
- An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition by William Feller in Front Matter
- Brownian Motion and Classical Potential Theory (Probability & Mathematical Statistics) by Sidney C. Port on page 445
See all 8 books this book cites
- An Introduction to Markov Processes (Graduate Texts in Mathematics) by Daniel W. Stroock in Back Matter
- Stochastic Approximation and Recursive Algorithms and Applications (Stochastic Modelling and Applied Probability) (v. 35) by Harold J. Kushner in Back Matter
- An Introduction to the Analysis of Paths on a Riemannian Manifold (Mathematical Surveys and Monographs) by Daniel W. Stroock in Back Matter
- Computational Learning Theory: 4th European Conference, EuroCOLT'99 Nordkirchen, Germany, March 29-31, 1999 Proceedings (Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence) by Paul Fischer on page 240
- An Introduction to Markov Processes (Graduate Texts in Mathematics) by Daniel W. Stroock in Back Matter
See all 15 books citing this book
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