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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Charles Ashbacher (CharlesAshbacher)
Charlie Ashbacher is a compulsive reader and writer about many subjects. His prime areas of expertise are in mathematics and computers where he has taught every course in the mathematics and computer … more
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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