This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, ergodic theory, weak convergence of probability measures, stationary stochastic processes, and the Kalman-Bucy filter. Many examples are discussed in detail, and there are a large number of exercises. The book is accessible to advanced undergraduates and can be used as a text or for self-study.The third edition contains new problems and exercises, new proofs, expanded material on financial mathematics, financial engineering, and mathematical statistics, and a final chapter on the history of probability theory.

From the contents:§Preface.- Sequences and Sums of Independent Random Variables.- Stationary (Strict Sense) Random Sequences and Ergodic Theory.- Stationary (Wide Sense) Random Sequences.- L2 Theory.- Sequences of Random Variables that Form Martingales.- Sequences of Random Variables that Form Markov Chains.- History of Mathematical Theory of Probability.- Bibliography (Chapters IV-VIII).- List of Literature.- Index.

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