Random number generation and Monte Carlo methods.

*(English)*Zbl 1028.65004
Statistics and Computing (Cham). New York, NY: Springer. xv, 381 p. (2003).

This is the second edition of the textbook on random number generation and Monte Carlo methods by James E. Gentle, see Zbl 0972.65003 for the first edition (1998).

The author provides a thorough survey of techniques of random number generation and the use of random numbers in Monte Carlo simulation. In the book basic principles are presented and, in addition, newer methods such as parallel random number generation, nonlinear congruential generators, quasi Monte Carlo methods, and Markov chain Monte Carlo. This second edition is approximately 50 testing of random number generators has been extended, it now provides more details about the tests and a discussion of recent software for testing. The section on applications of Monte Carlo methods has also been expanded and includes, e.g., material on computational physics and finance.

The book contains a large bibliography (updated for the second edition) including WWW links and it could serve as the primary text or a supplementary text for various courses in computational statistics and other areas that rely on Monte Carlo simulation, e.g. numerical methods for stochastic differential equations or computational finance.

The author provides a thorough survey of techniques of random number generation and the use of random numbers in Monte Carlo simulation. In the book basic principles are presented and, in addition, newer methods such as parallel random number generation, nonlinear congruential generators, quasi Monte Carlo methods, and Markov chain Monte Carlo. This second edition is approximately 50 testing of random number generators has been extended, it now provides more details about the tests and a discussion of recent software for testing. The section on applications of Monte Carlo methods has also been expanded and includes, e.g., material on computational physics and finance.

The book contains a large bibliography (updated for the second edition) including WWW links and it could serve as the primary text or a supplementary text for various courses in computational statistics and other areas that rely on Monte Carlo simulation, e.g. numerical methods for stochastic differential equations or computational finance.

Reviewer: Evelyn Buckwar (Berlin)

##### MSC:

65C10 | Random number generation in numerical analysis |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |

65C05 | Monte Carlo methods |

11K45 | Pseudo-random numbers; Monte Carlo methods |

60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |

65C30 | Numerical solutions to stochastic differential and integral equations |

91G60 | Numerical methods (including Monte Carlo methods) |