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Simulation and the Monte Carlo Method, Student Solutions Manual, 2nd Edition

ISBN: 978-0-470-28530-5
208 pages
January 2012
Simulation and the Monte Carlo Method, Student Solutions Manual, 2nd Edition (0470285303) cover image
This accessible new edition explores the major topics in Monte Carlo simulation

Simulation and the Monte Carlo Method, Second Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte Carlo simulation since the publication of the classic First Edition over twenty-five years 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 the transform likelihood ratio method and the screening 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 to rare events estimation and combinatorial optimization
  • Application of Monte Carlo techniques for counting problems, with an emphasis on the parametric minimum cross-entropy method

An extensive range of exercises is provided at the end of each chapter, with more difficult sections and exercises marked accordingly for advanced readers. A generous sampling of applied examples is positioned throughout the book, emphasizing various areas of application, and a detailed appendix presents an introduction to exponential families, a discussion of the computational complexity of stochastic programming problems, and sample MATLAB programs.

Requiring only a basic, introductory knowledge of probability and statistics, Simulation and the Monte Carlo Method, Second Edition is an excellent text for upper-undergraduate and beginning graduate courses in 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.

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Preface.

Acknolwedgments.

I: Problems.

1. Preliminaries.

2. Random Number, random Variable, and Stochastic Process Generation.

3. Simulatin of Discrete-Event Systems.

4. Stastical Analysis of Discrete-Event Systems.

5. Controlling the Variance.

6. Markov Chain Monte Carlo.

7. Sensitivity Analysis and Monte Carlo Optimization.

8. The Cross-Entropy Method.

9. Counting via Monte Carlo.

10. Appendix.

II: Solutions.

11. Prelimiaries.

12. Random Number, Random Variable, and Stochastic Process Generation.

13. Simulatin of Discrete-Event Systems.

14. Stastical Analysis of Discrete-Event Systems.

15. Controlling the Variance.

16. Markov Chain Monte Carlo.

17. Sensitivity Analysis and Monte Carlo Optimization.

18. The Cross-Entropy Method.

19. Counting via Monte Carlo.

20. Appendix.

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  • This long awaited second edition gives a fully updated and comprehensive account of the major topics in Monte Carlo simulation since the early 1980's.
  • The basic concepts of probability, Markov processes, and convex optimization are now carefully reviewed in a completely revised Chapter.
  • A new co-author has been added to enliven the writing style and to provide modern day expertise .
  • The authors aim to provide an accessible introduction to modern MCM, focusing on the main concepts, while providing a sound foundation for problem solving.
  • Most ideas are introduced and explained by way of concrete examples, algorithms, and practical experiments.
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  • An extensive range of exercises is provided at the end of each chapter. More difficult sections and exercises are marked accordingly.
  • Examples of cross-entropy programs, written in Matlab, are given in an appendix.
  • A generous sampling of applied examples are positioned throughout the book emphasizing areas such as engineering, computer science, finance, statistics, and the physical and life sciences.
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