LEADER 05233nam 2200637Ia 450 001 9910830283103321 005 20230105194502.0 010 $a1-62198-230-0 010 $a1-282-68811-1 010 $a9786612688119 010 $a3-527-62621-2 010 $a3-527-62622-0 035 $a(CKB)1000000000766585 035 $a(EBL)481869 035 $a(OCoLC)437248491 035 $a(SSID)ssj0000340551 035 $a(PQKBManifestationID)11947677 035 $a(PQKBTitleCode)TC0000340551 035 $a(PQKBWorkID)10387952 035 $a(PQKB)10860025 035 $a(MiAaPQ)EBC481869 035 $a(EXLCZ)991000000000766585 100 $a20080430d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMonte Carlo methods$b[electronic resource] /$fMalvin H. Kalos, Paula A. Whitlock 205 $a2nd ed. 210 $aWeinheim $cWiley-Blackwell$dc2008 215 $a1 online resource (217 p.) 300 $aPrevious ed.: New York; Chichester: Wiley 1986. 311 $a3-527-40760-X 320 $aIncludes bibliographical references and index. 327 $aMonte Carlo Methods; Contents; Preface to the Second Edition; Preface to the First Edition; 1 What is Monte Carlo?; 1.1 Introduction; 1.2 Topics to be Covered; 1.3 A Short History of Monte Carlo; References; 2 A Bit of Probability; 2.1 Random Events; 2.2 Random Variables; 2.2.1 The Binomial Distribution; 2.2.2 The Geometric Distribution; 2.2.3 The Poisson Distribution; 2.3 Continuous Random Variables; 2.4 Expectations of Continuous Random Variables; 2.5 Bivariate Continuous Random Distributions; 2.6 Sums of Random Variables: Monte Carlo Quadrature 327 $a2.7 Distribution of the Mean of a Random Variable: A Fundamental Theorem2.8 Distribution of Sums of Independent Random Variables; 2.9 Monte Carlo Integration; 2.10 Monte Carlo Estimators; References; Further Reading; Elementary; More Advanced; 3 Sampling Random Variables; 3.1 Transformation of Random Variables; 3.2 Numerical Transformation; 3.3 Sampling Discrete Distributions; 3.4 Composition of Random Variables; 3.4.1 Sampling the Sum of Two Uniform Random Variables; 3.4.2 Sampling a Random Variable Raised to a Power; 3.4.3 Sampling the Distribution f(z) = z(1 - z) 327 $a3.4.4 Sampling the Sum of Several Arbitrary Distributions3.5 Rejection Techniques; 3.5.1 Sampling a Singular pdf Using Rejection; 3.5.2 Sampling the Sine and Cosine of an Angle; 3.5.3 Kahn's Rejection Technique for a Gaussian; 3.5.4 Marsaglia et al. Method for Sampling a Gaussian; 3.6 Multivariate Distributions; 3.6.1 Sampling a Brownian Bridge; 3.7 The M(RT)2 Algorithm; 3.8 Application of M(RT)2; 3.9 Testing Sampling Methods; References; Further Reading; 4 Monte Carlo Evaluation of Finite-Dimensional Integrals; 4.1 Importance Sampling; 4.2 The Use of Expected Values to Reduce Variance 327 $a4.3 Correlation Methods for Variance Reduction4.3.1 Antithetic Variates; 4.3.2 Stratification Methods; 4.4 Adaptive Monte Carlo Methods; 4.5 Quasi-Monte Carlo; 4.5.1 Low-Discrepancy Sequences; 4.5.2 Error Estimation for Quasi-Monte Carlo Quadrature; 4.5.3 Applications of Quasi-Monte Carlo; 4.6 Comparison of Monte Carlo Integration, Quasi-Monte Carlo and Numerical Quadrature; References; Further Reading; 5 Random Walks, Integral Equations, and Variance Reduction; 5.1 Properties of Discrete Markov Chains; 5.1.1 Estimators and Markov Processes; 5.2 Applications Using Markov Chains 327 $a5.2.1 Simulated Annealing5.2.2 Genetic Algorithms; 5.2.3 Poisson Processes and Continuous Time Markov Chains; 5.2.4 Brownian Motion; 5.3 Integral Equations; 5.3.1 Radiation Transport and Random Walks; 5.3.2 The Boltzmann Equation; 5.4 Variance Reduction; 5.4.1 Importance Sampling of Integral Equations; References; Further Reading; 6 Simulations of Stochastic Systems: Radiation Transport; 6.1 Radiation Transport as a Stochastic Process; 6.2 Characterization of the Source; 6.3 Tracing a Path; 6.4 Modeling Collision Events; 6.5 The Boltzmann Equation and Zero Variance Calculations 327 $a6.5.1 Radiation Impinging on a Slab 330 $aThis introduction to Monte Carlo methods seeks to identify and study the unifying elements that underlie their effective application. Initial chapters provide a short treatment of the probability and statistics needed as background, enabling those without experience in Monte Carlo techniques to apply these ideas to their research.The book focuses on two basic themes: The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and impor 606 $aMonte Carlo method$vProblems, exercises, etc 606 $aMonte Carlo method 615 0$aMonte Carlo method 615 0$aMonte Carlo method. 676 $a518.282 700 $aKalos$b Malvin H$0294629 701 $aWhitlock$b Paula A$0308051 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830283103321 996 $aMonte Carlo methods$9739067 997 $aUNINA