The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis has been just intuitively explained in the text, but is developed in detail at the level of advanced calculus in the numerous solved theoretical problems. The 2nd Edition includes two new chapters with a thorough coverage of the central ideas of Bayesian and classical statistics.
Develops the basic concepts of probability, random variables, stochastic processes, laws of large numbers, and the central limit theorem. Provides many theoretical problems that extend the book's coverage and enhance its mathematical foundation solutions are included in the text. Provides many problems that enhance the understanding of the basic material, together with web-posted solutions. Is supplemented by additional web-based unsolved problems. Has been developed through extensive classroom use and experience at the Massachusetts Institute of Technology. This book explains every single concept it enunciates.
Knight, Mathematical Reviews.
International Encyclopedia of Unified Science
Scheutzow, Zentralblatt. Yet this is precisely what Professor Kallenberg has attempted in the volume under review and he has accomplished it brilliantly. Getoor, Metrica.
For the second edition … Professor Kallenberg has added over a hundred pages in attempt to keep it up to date with the exponentially increasing body of knowledge which is probability theory. Moreover, certain sections … have been comprehensively rewritten in order to be self-sufficient. The second edition is a revised and enlarged version of the first ….
Introduction to Probability, 2nd Edition
Of course, the praise for the first edition applies to the second edition as well. Nevertheless, it should be noted that the style in which this monograph is written is concise and particular. It has been said that the present monograph is a modern classic in probability theory, and this is true. Schmidt, Mathematical Reviews, Issue m.
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Probability and Its Applications. Buy Hardcover.
Processes, Distributions, and Independence Pages Random Sequences, Series, and Averages Pages Conditioning and Disintegration Pages Martingales and Optional Times Pages Random Walks and Renewal Theory Pages Stationary Processes and Ergodic Theory Pages Gaussian Processes and Brownian Motion Pages Skorohod Embedding and Invariance Principles Pages Independent Increments and Infinite Divisibility Pages Stochastic Integrals and Quadratic Variation Pages Continuous Martingales and Brownian Motion Pages