Preface.- 1. Elementary Probability Theory.- 2. Mathematical Foundations of Probability Theory.- 3. Convergence of Probability Measures.- 4. Independent Random Variables.- 5. Stationary Random Sequences in Strict Sense.- 6. Stationary Random Sequences in Broad Sense.- 7. Martingales.- 8. Markov Chains.- Appendix.- References.
Albert Shiryaev is an eminent mathematician who has written several texts on probability and stochastic calculus, which have been translated into several languages. He is the recipient of several honors and awards, including the Humboldt Research Award, Markov prize, and Kolmogorov prize.
From the book reviews:“The present book is a rich and comprehensive collection of problems compiled over many years for use in graduate courses at Moscow State University and other academic institutions in Russia. … Problems in Probability is an excellent source of exercises for graduate courses in probability. The exercises are diverse and very well chosen … .” (SIAM Review, Vol. 56 (4), December, 2014)“This is an invaluable addition to the class of problem books; it will enable the beginning graduate student to tackle the more advanced continuous time counterparts of the material therein presented. It can also be used as a reference for specific results.” (Giuseppe Castellacci, Mathematical Reviews, January, 2014)“The book includes a wide variety of problems that Shiryaev has written himself and collected from other ‘textbooks, lecture notes, exercise manuals, monographs, research papers, private communications, and such.’ … will serve as a good reference for readers who have already seen the topics. … Shiryaev’s book provides an excellent source of problems and will be a valuable resource to students who wish to learn probability at the graduate level.” (Darren Glass, MAA Reviews, June, 2013)“This eight-chapter book contains problems on various aspects of probability that Shiryaev … carefully collected from diverse sources or created himself. … An attractive feature is the inclusion of hints/suggestions accompanying some of the difficult problems. … well-written book could be gainfully used as a supplementary text for an advanced course in probability theory or mathematics of finance. Researchers in probability would also find the book helpful. Summing Up: Highly recommended. Libraries serving universities with a strong program in probability theory; upper-division undergraduates through researchers/faculty.” (D. V. Chopra, Choice, Vol. 50 (8), April, 2013)
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