Probability: A Graduate Course: 75 2nd ed. 2013 Edition

From the reviews of the second edition:

“This book of over 600 pages gives a self-contained presentation of modern probability theory. This is an updated edition of an elementary introductory book on probability theory … . Suitable as a textbook for beginning students in mathematics, statistics, computer science or economics … . Also, it will be very useful to students and researchers in mathematics or theoretical physics.” (Teodora-Liliana Rădulescu, zbMATH, Vol. 1267, 2013)

Like its predecessor, this book starts from the premise that, rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book 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 a thorough treatment of the three main subjects in probability theory: 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 new edition is comprehensively updated, including some new material as well as around a dozen new references.