http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
A comprehensive overview of Monte Carlo simulation that explores the latest topics, techniques, and real-world applications. More and more of today's numerical problems found in engineering and finance are solved through Monte Carlo methods. The heightened popularity of these methods and their continuing development makes it important for researchers to have a comprehensive understanding of the Monte Carlo approach. Handbook of Monte Carlo Methods provides the theory, algorithms, and applications that helps provide a thorough understanding of the emerging dynamics of this rapidly-growing field. The authors begin with a discussion of fundamentals such as how to generate random numbers on a computer. Subsequent chapters discuss key Monte Carlo topics and methods, including: Random variable and stochastic process generation, Markov chain Monte Carlo, featuring key algorithms such as the Metropolis-Hastings method, the Gibbs sampler, and hit-and-run, Discrete-event simulation, Techniques for the statistical analysis of simulation data including the delta method, steady-state estimation, and kernel density estimation, Variance reduction, including importance sampling, latin hypercube sampling, and conditional Monte Carlo, Estimation of derivatives and sensitivity analysis. Advanced topics including cross-entropy, rare events, kernel density estimation, quasi Monte Carlo, particle systems, and randomized optimization. The presented theoretical concepts are illustrated with worked examples that use MATLAB® a related Web site houses the MATLAB® code, allowing readers to work hands-on with the material. Detailed appendices provide background material on probability theory, stochastic processes, and mathematical statistics as well as the key optimization concepts and techniques that are relevant to Monte Carlo simulation.
Cover13; -- Contents -- Preface -- Acknowledgments -- 1 Uniform Random Number Generation -- 1.1 Random Numbers -- 1.1.1 Properties of a Good Random Number Generator -- 1.1.2 Choosing a Good Random Number Generator -- 1.2 Generators Based on Linear Recurrences -- 1.2.1 Linear Congruential Generators -- 1.2.2 Multiple-Recursive Generators -- 1.2.3 Matrix Congruential Generators -- 1.2.4 Modulo 2 Linear Generators -- 1.3 Combined Generators -- 1.4 Other Generators -- 1.5 Tests for Random Number Generators -- 1.5.1 Spectral Test -- 1.5.2 Empirical Tests -- References -- 2 Quasirandom Number Generation -- 2.1 Multidimensional Integration -- 2.2 Van der Corput and Digital Sequences -- 2.3 Halton Sequences -- 2.4 Faure Sequences -- 2.5 Sobol' Sequences -- 2.6 Lattice Methods -- 2.7 Randomization and Scrambling -- References -- 3 Random Variable Generation -- 3.1 Generic Algorithms Based on Common Transformations -- 3.1.1 Inverse-Transform Method -- 3.1.2 Other Transformation Methods -- 3.1.3 Table Lookup Method -- 3.1.4 Alias Method -- 3.1.5 Acceptance-Rejection Method -- 3.1.6 Ratio of Uniforms Method -- 3.2 Generation Methods for Multivariate Random Variables -- 3.2.1 Copulas -- 3.3 Generation Methods for Various Random Objects -- 3.3.1 Generating Order Statistics -- 3.3.2 Generating Uniform Random Vectors in a Simplex -- 3.3.3 Generating Random Vectors Uniformly Distributed in a Unit Hyperball and Hypersphere -- 3.3.4 Generating Random Vectors Uniformly Distributed in a Hyperellipsoid -- 3.3.5 Uniform Sampling on a Curve -- 3.3.6 Uniform Sampling on a Surface -- 3.3.7 Generating Random Permutations -- 3.3.8 Exact Sampling From a Conditional Bernoulli Distribution -- References -- 4 Probability Distributions -- 4.1 Discrete Distributions -- 4.1.1 Bernoulli Distribution -- 4.1.2 Binomial Distribution -- 4.1.3 Geometric Distribution -- 4.1.4 Hypergeometric Distribution -- 4.1.5 Negative Binomial Distribution -- 4.1.6 Phase-Type Distribution (Discrete Case) -- 4.1.7 Poisson Distribution -- 4.1.8 Uniform Distribution (Discrete Case) -- 4.2 Continuous Distributions -- 4.2.1 Beta Distribution -- 4.2.2 Cauchy Distribution -- 4.2.3 Exponential Distribution -- 4.2.4 F Distribution -- 4.2.5 Fr233;chet Distribution -- 4.2.6 Gamma Distribution -- 4.2.7 Gumbel Distribution -- 4.2.8 Laplace Distribution -- 4.2.9 Logistic Distribution -- 4.2.10 Log-Normal Distribution -- 4.2.11 Normal Distribution -- 4.2.12 Pareto Distribution -- 4.2.13 Phase-Type Distribution (Continuous Case) -- 4.2.14 Stable Distribution -- 4.2.15 Student's t Distribution -- 4.2.16 Uniform Distribution (Continuous Case) -- 4.2.17 Wald Distribution -- 4.2.18 Weibull Distribution -- 4.3 Multivariate Distributions -- 4.3.1 Dirichlet Distribution -- 4.3.2 Multinomial Distribution -- 4.3.3 Multivariate Normal Distribution -- 4.3.4 Multivariate Student's t Distribution -- 4.3.5 Wishart Distribution -- References -- 5 Random Process Generation -- 5.1 Gaussian Processes -- 5.1.1 Markovian Gaussian Processes -- 5.1.2 Stationary Gaussian Processes and the FFT -- 5.2 Markov Chains -- 5.3 Markov Jump Processes -- 5.4 Poisson Processes -- 5.4.1 Compound Poisson Process -- 5.5 Wiener Process and Brownian Motion -- 5.6 Stochastic Differential Eq.
Dirk P. Kroese, Thomas Taimre, Zdravko I. Botev.
Includes bibliographical references and index.
Wiley series in probability and statistics ; 706