Handbook of monte carlo methods /

• Κύριοι συγγραφείς: Kroese, Dirk P., Taimre, Thomas (Συγγραφέας), Botev, Zdravko I. (Συγγραφέας)
• Μορφή: Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: [Place of publication not identified] : Wiley, 2011.
• Σειρά: Wiley series in probability and statistics ; 706.
• Θέματα: Monte Carlo method > Handbooks, manuals, etc.; Monte Carlo method.; MATHEMATICS > Probability & Statistics > General.; MATHEMATICS > Numerical Analysis.; Electronic resource.; Electronic books.; Handbooks and manuals.

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...

Πίνακας περιεχομένων:

• 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.