This two-volume textbook set presents a systematic treatment of probability from the ground up. It begins with intuitive ideas and gradually develops more sophisticated subjects, such as random walks, martingales, Markov chains, the measure-theoretic foundations of probability theory, weak convergence of probability measures, and the central limit theorem. Numerous detailed examples and exercises are provided throughout. In addition to the thorough presentation of probability, a historical exposition is presented that documents how the mathematical theory of probability has developed.
The two volumes that compose this set together constitute the third English edition of the author’s classic, Probability. The first volume is particularly suitable for a graduate course on probability aimed at mathematics, statistics, or engineering students, and the second volume would be ideal for a graduate course on random process.