Probability theory has recently become more important as an area of study and research. This set of exercises can be used for classroom teaching or independent study and will help students reach the level where they can begin to tackle current research. It includes outline answers to all the problems and numerous references to the literature.
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Editorial Reviews
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"...a very appealing and valuable book for independent study or as a companion book in advanced probability theory courses. Highly recommended." Choice
"This is an excellent book, which should be in every library, and also on the bookshelf of anyone with interests in advanced probability and random processes." SIAM Review
"...a magnificent resource, not just in terms of shearing recent research results to their core but in encouraging putative researchers to think of an interplay between finite and infinite dimensional viewpoints for a given problem. In that sense, the authors take us into the mind of the researcher...For beginning researchers in stochastic mathematics, this book comes highly recommended and libraries should obtain a copy." Journal of the Royal Statistical Society
"This is an excellent book, which should be in every library, and also on the bookshelf of anyone with interests in advanced probability and random processes." SIAM Review
"...a magnificent resource, not just in terms of shearing recent research results to their core but in encouraging putative researchers to think of an interplay between finite and infinite dimensional viewpoints for a given problem. In that sense, the authors take us into the mind of the researcher...For beginning researchers in stochastic mathematics, this book comes highly recommended and libraries should obtain a copy." Journal of the Royal Statistical Society
Book Description
Probability theory has recently become more important as an area of study and research. However, it is often the case that graduate classes are quite small and students will need to learn independently. This set of exercises can be used for classroom teaching or independent study and will help students rea ch the level where they can begin to tackle current research. The book is based on the authors' teaching in Paris, where probability is extremely strong. There are outline answers to all the problems, and numerous references to the literature.
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Most Helpful Customer Reviews
2 of 2 people found the following review helpful:
5.0 out of 5 stars
An excellent tool for self-study for the student with the proper background,
By Charles Ashbacher (Marion, Iowa United States) - See all my reviews (TOP 500 REVIEWER) (VINE VOICE) (HALL OF FAME REVIEWER)
This review is from: Exercises in Probability: A Guided Tour from Measure Theory to Random Processes, via Conditioning (Cambridge Series in Statistical and Probabilistic Mathematics) (Hardcover)
This set of solved problems involves measure theory and probability and the level of difficulty is that of the Ph. D. student. The problems delve deeply into the theory of probability, independence, Gaussian variables, distributed computations and random processes. There are approximately 100 problems and nearly complete solutions to all of them are included. There is a statement on the back cover that many of the problems can lead the student on to research topics in probability and I fully agree with that.
The chapter headings are: *) Measure theory and probability *) Independence and conditioning *) Gaussian variables *) Distributional computations *) Convergence of random variables *) Random processes This is an excellent self-study guide for the student that wants problems that will push them to the very edge of research in probability.
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Inside This Book
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First Sentence:
This chapter contains a number of exercises, aimed at familiarizing the reader with some important measure theoretic concepts, such as: Monotone Class Theorem (Williams [63], II.3, II.4, II.13), uniform integrability (which is often needed when working with a family of probabilities, see Dellacherie and Meyer [16]), Lp convergence (Jacod and Protter [29], Chapter 23), conditioning (this will be developed in a more probabilistic manner in the following chapters), absolute continuity (Fristedt and Gray [25], p. 118). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
affine process, optional stopping theorem, gamma variables, joint law, deduce therefrom, conditional law, gaussian variable, exponential variable, independence hypothesis, above identity, analytical continuation, scaling property, probability space Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Monotone Class Theorem, London Math, Ergodic Theory, Probability Solution New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter contains a number of exercises, aimed at familiarizing the reader with some important measure theoretic concepts, such as: Monotone Class Theorem (Williams [63], II.3, II.4, II.13), uniform integrability (which is often needed when working with a family of probabilities, see Dellacherie and Meyer [16]), Lp convergence (Jacod and Protter [29], Chapter 23), conditioning (this will be developed in a more probabilistic manner in the following chapters), absolute continuity (Fristedt and Gray [25], p. 118). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
affine process, optional stopping theorem, gamma variables, joint law, deduce therefrom, conditional law, gaussian variable, exponential variable, independence hypothesis, above identity, analytical continuation, scaling property, probability space Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Monotone Class Theorem, London Math, Ergodic Theory, Probability Solution 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 46
books:
See all 46 books this book cites
- Foundations of Modern Probability by Olav Kallenberg on page 31, and Back Matter
- Aspects of Brownian Motion (Universitext) by Roger Mansuy on page 192, and Back Matter
- Ergodic Theory (Cambridge Studies in Advanced Mathematics) by Karl E. Petersen on page 7, and Back Matter
- Bayesian Methods: An Analysis for Statisticians and Interdisciplinary Researchers (Cambridge Series in Statistical and Probabilistic Mathematics) by Thomas Leonard in Front Matter
- Probabilistic Methods in the Theory of Numbers (Translations of Mathematical Monographs) by J. Kubilius on page 35
See all 46 books this book cites
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