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Successfully synthesizes the most important classical ideas and results with many of the major achievements of modern probability theory
Author provides clear and comprehensive introduction to probability theory
Third edition now has a chapter on the history of probability theory
Covers in detail topics including ergodic theory, weak convergence of probability measures, stationary stochastic processes, and the Kalman-Bucy filter
Advanced maths students have been waiting for this, the third edition of a text that deals with one of the fundamentals of their field.
Shiryaev’s brilliant treatment of the subject successfully synthesizes the most important classical ideas and results with many of the major achievements of modern probability theory.
The 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, and Markov chains.
The author also covers in detail topics including ergodic theory, weak convergence of probability measures, stationary stochastic processes, and the Kalman-Bucy filter.
Many examples are discussed in depth, and there are a large number of exercises.
The book 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.
It also now has a final chapter on the history of probability theory.
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.