## Simulation and the Monte Carlo MethodThis accessible new edition explores the major topics in Monte Carlo simulation
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, |

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### Contents

Random Number Random Variable | |

Problems | |

Simulation of DiscreteEvent Systems | |

Counting viaMonte Carlo | |

Markov ChainMonte Carlo | |

Statistical Analysisof DiscreteEvent Systems 4 1 Introduction 4 2 Static Simulation Models | |

Controlling theVariance | |

Problems | |

Sensitivity Analysisand MonteCarlo Optimization | |

The CrossEntropy Method | |

and Decision Making 9 7 Numerical Results | |

Appendix | |

Sensitivity Analysis | |

Abbreviations and Acronyms | |