Simulation and the Monte Carlo method / Reuven Y. Rubinstein y Dirk P. Kroese.

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1 Preliminaries -- 2 Random Number, Random Variable, and Stochastic Process Generation -- 3 Simulation of Discrete-Event Systems -- 4 Statistical Analysis of Discrete-Event Systems -- 5 Controlling the Variance -- 6 Markov Chain Monte Carlo -- 7 Sensitivity Analysis and Monte Carlo Optimization -- 8 Cross-Entropy Method -- 9 Splitting Method -- 10 Stochastic Enumeration Method.

Simulation and the Monte Carlo Method, Third Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the state-of-the-art theory, methods and applications that have emerged in Monte Carlo simulation since the publication of the classic First Edition over more than a quarter of a century ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences. The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including: Markov Chain Monte Carlo, variance reduction techniques such as importance (re-)sampling, and the transform likelihood ratio method, the score function method for sensitivity analysis, the stochastic approximation method and the stochastic counter-part method for Monte Carlo optimization, the cross-entropy method for rare events estimation and combinatorial optimization, and application of Monte Carlo techniques for counting problems. An extensive range of exercises is provided at the end of each chapter, as well as a generous sampling of applied examples.

The Third Edition features a new chapter on the highly versatile splitting method, with applications to rare-event estimation, counting, sampling, and optimization. A second new chapter introduces the stochastic enumeration method, which is a new fast sequential Monte Carlo method for tree search. In addition, the Third Edition features new material on:

• Random number generation, including multiple-recursive generators and the Mersenne Twister

• Simulation of Gaussian processes, Brownian motion, and diffusion processes

• Multilevel Monte Carlo method

• New enhancements of the cross-entropy (CE) method, including the “improved” CE method, which uses sampling from the zero-variance distribution to find the optimal importance sampling parameters

• Over 100 algorithms in modern pseudo code with flow control

• Over 25 new exercises

Simulation and the Monte Carlo Method, Third Edition is an excellent text for upper-undergraduate and beginning graduate courses in stochastic simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method. El texto.

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