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Mathematics - Probability Theory and Stochastic Processes | Probability - Volume 2

Probability

Volume 2

Series: Graduate Texts in Mathematics, Vol. 95

Volume package: Probability

Shiryaev, Albert

Translated by Chibisov, D.M.

Originally published in one volume

3rd ed. 2015, XX, 480 p. 7 illus.

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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.

Content Level » Graduate

Related subjects » Probability Theory and Stochastic Processes

Table of 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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