Probability: A Graduate Course
This textbook on the theory of probability is aimed at graduate students. It starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by explanations of the three main subjects in probability: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales. The main feature of this book is the combination of rigor and detail. Instead of leaving lots of technicalities to be filled in by the reader or dealt with as exercises, the text has a more solid foundation as a result of a detailed exploration of more complex concepts.
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