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**Elementary probability theory. With stochastic processes and an introduction to mathematical finance.
4th rev. ed.**
*(English)*
Zbl 1019.60001

Undergraduate Texts in Mathematics. New York, NY: Springer. xiii, 402 p. (2003).

This is the fourth edition of the classical introductory textbook by K. L. Chung. See Zbl 0159.45701 for a review of the first edition (1968), Zbl 0345.60003 for the second edition (1974), Zbl 0980.60001 for the third edition (2000).

This textbook is very popular among those who teach probability theory as well as among those who study probability theory. It is a well organized and clear written elementary introduction to probability theory with lots of exercises, examples and applications. Basic concepts such as probability measure, random variable, distribution, and expectation are treated without technical complications. Only the elements of calculus are used. The emphasis is on probabilistic reasoning, explained and illustrated with a large number of carefully selected examples. Special topics include: combinatorial problems, urn schemes, Poisson processes, random walks, and Markov chains. Problems and solutions are provided at the end of each chapter. Its elementary nature makes this a useful text not only for mathematicians, but also for students in engineering and the physical, biological, and social sciences.

This edition adds two self-contained chapters with introductory material on mathematical finance. Elements of modern portfolio and option pricing theories are presented in a detailed manner. Numerous graded and motivated examples and exercises are supplied to illustrate the applicability of the fundamental concepts and techniques to concrete financial problems. The approach distinguishes this text from others, which are either too mathematically advanced or cover significantly more finance topics at the expense of mathematical rigor. An introductory discussion on stable laws in an applied context is also included.

This textbook is very popular among those who teach probability theory as well as among those who study probability theory. It is a well organized and clear written elementary introduction to probability theory with lots of exercises, examples and applications. Basic concepts such as probability measure, random variable, distribution, and expectation are treated without technical complications. Only the elements of calculus are used. The emphasis is on probabilistic reasoning, explained and illustrated with a large number of carefully selected examples. Special topics include: combinatorial problems, urn schemes, Poisson processes, random walks, and Markov chains. Problems and solutions are provided at the end of each chapter. Its elementary nature makes this a useful text not only for mathematicians, but also for students in engineering and the physical, biological, and social sciences.

This edition adds two self-contained chapters with introductory material on mathematical finance. Elements of modern portfolio and option pricing theories are presented in a detailed manner. Numerous graded and motivated examples and exercises are supplied to illustrate the applicability of the fundamental concepts and techniques to concrete financial problems. The approach distinguishes this text from others, which are either too mathematically advanced or cover significantly more finance topics at the expense of mathematical rigor. An introductory discussion on stable laws in an applied context is also included.

Reviewer: Mikhail P.Moklyachuk (Kyïv)

### MSC:

60-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |