Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage. The first half of the book focuses on general methods, whereas the second half discusses model-specific algorithms.

"The book covers a broad aspect of topics and applications in simulation at a higher mathematical level than other recent texts in the area. Its readership is intended for graduate students and researchers from a broad variety of areas, in particular applied probability, statistics, mathematical finance, operations research, industrial engineering, electrical engineering and other application areas. The book contains a large amount of exercises and illustrations. TOC:What this Book is about.- Part A: General Methods and Algorithms.- Generating Random Objects.- Output Analysis.- Steady-State Simulation.- Variance Reduction Methods.- Rare Event Simulation.- Gradient Estimation.- Stochastic Optimization.- Part B: Algorithms for Special Models.- Numerical Integration.- Stochastic Differential Equations.- Gaussian Processes.- Lévy Processes.- Markov Chain Monte Carlo Methods.- Selected Topics and Extended Examples.- Appendix.- Bibliography.- Index."

General Methods and Algorithms.- Generating Random Objects.- Output Analysis.- Steady-State Simulation.- Variance-Reduction Methods.- Rare-Event Simulation.- Derivative Estimation.- Stochastic Optimization.- Algorithms for Special Models.- Numerical Integration.- Stochastic Di3erential Equations.- Gaussian Processes.- Lèvy Processes.- Markov Chain Monte Carlo Methods.- Selected Topics and Extended Examples.- What This Book Is About.- What This Book Is About.