<h1 eaggd="0" lohuf="0"><div class="buying"><font size="3"><b class="sans"><span id="btAsinTitle">Stochastic Simulation: Algorithms and Analysis (Stochastic Modelling and Applied Probability) (Hardcover)</span><!--Element not supported - Type: 8 Name: #comment--></b><br/></font><font size="2">by </font><a href="http://www.amazon.com/exec/obidos/search-handle-url?%5Fencoding=UTF8&amp;search-type=ss&amp;index=books&amp;field-author=S%C3%B8ren%20Asmussen"><font color="#003399" size="2">S&oslash;ren Asmussen</font></a><font size="2"> (Author), </font><a href="http://www.amazon.com/exec/obidos/search-handle-url?%5Fencoding=UTF8&amp;search-type=ss&amp;index=books&amp;field-author=Peter%20W.%20Glynn"><font color="#003399" size="2">Peter W. Glynn</font></a><font size="2"> (Author)</font>
</div></h1><p><b>Hardcover:</b> 482 pages </p><p><b>Publisher:</b> Springer; 1 edition (July 27, 2007) </p><p><b>Language:</b> English </p><p><b>ISBN-10:</b> 038730679X </p><div class="content"><b>Book Description</b><br/><p>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.</p><p>Given the wide range of examples, exercises and applications students, practitioners and researchers in probability, statistics, operations research, economics, finance, engineering as well as biology and chemistry and physics will find the book of value.</p><p>S&oslash;ren Asmussen is Professor of Applied Probability at Aarhus University, Denmark and Peter Glynn is Thomas Ford Professor of Engineering at Stanford University.</p><p></p><p><strong>Contents</strong></p><p><strong></strong><br/>Preface v<br/>Notation xii<br/>I What This Book Is About 1<br/>1 An Illustrative Example: The Single-Server Queue . . . 1<br/>2 TheMonte CarloMethod . . . . . . . . . . . . . . . . 5<br/>3 Second Example: Option Pricing . . . . . . . . . . . . . 6<br/>4 Issues Arising in the Monte Carlo Context . . . . . . . 9<br/>5 Further Examples . . . . . . . . . . . . . . . . . . . . . 13<br/>6 Introductory Exercises . . . . . . . . . . . . . . . . . . 25<br/>Part A: General Methods and Algorithms 29<br/>II Generating Random Objects 30<br/>1 Uniform RandomVariables . . . . . . . . . . . . . . . . 30<br/>2 NonuniformRandomVariables . . . . . . . . . . . . . . 36<br/>3 Multivariate Random Variables . . . . . . . . . . . . . 49<br/>4 Simple Stochastic Processes . . . . . . . . . . . . . . . 59<br/>5 Further Selected Random Objects . . . . . . . . . . . . 62<br/>6 Discrete-Event Systems and GSMPs . . . . . . . . . . 65<br/>III Output Analysis 68<br/>1 Normal Confidence Intervals . . . . . . . . . . . . . . . 68<br/>Contents ix<br/>2 Two-Stage and Sequential Procedures . . . . . . . . . . 71<br/>3 Computing Smooth Functions of Expectations . . . . . 73<br/>4 Computing Roots of Equations Defined by Expectations 77<br/>5 Sectioning, Jackknifing, and Bootstrapping . . . . . . . 80<br/>6 Variance/Bias Trade-Off Issues . . . . . . . . . . . . . 86<br/>7 Multivariate Output Analysis . . . . . . . . . . . . . . 88<br/>8 Small-Sample Theory . . . . . . . . . . . . . . . . . . . 90<br/>9 Simulations Driven by Empirical Distributions . . . . . 91<br/>10 The Simulation Budget . . . . . . . . . . . . . . . . . . 93<br/>IV Steady-State Simulation 96<br/>1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 96<br/>2 Formulas for the Bias and Variance . . . . . . . . . . . 102<br/>3 Variance Estimation for Stationary Processes . . . . . 104<br/>4 The RegenerativeMethod . . . . . . . . . . . . . . . . 105<br/>5 TheMethod of BatchMeans . . . . . . . . . . . . . . . 109<br/>6 Further Refinements . . . . . . . . . . . . . . . . . . . 110<br/>7 Duality Representations . . . . . . . . . . . . . . . . . 118<br/>8 Perfect Sampling . . . . . . . . . . . . . . . . . . . . . 120<br/>V Variance-Reduction Methods 126<br/>1 Importance Sampling . . . . . . . . . . . . . . . . . . . 127<br/>2 ControlVariates . . . . . . . . . . . . . . . . . . . . . . 138<br/>3 Antithetic Sampling . . . . . . . . . . . . . . . . . . . . 144<br/>4 ConditionalMonte Carlo . . . . . . . . . . . . . . . . . 145<br/>5 Splitting . . . . . . . . . . . . . . . . . . . . . . . . . . 147<br/>6 Common RandomNumbers . . . . . . . . . . . . . . . 149<br/>7 Stratification . . . . . . . . . . . . . . . . . . . . . . . . 150<br/>8 Indirect Estimation . . . . . . . . . . . . . . . . . . . . 155<br/>VI Rare-Event Simulation 158<br/>1 Efficiency Issues . . . . . . . . . . . . . . . . . . . . . . 158<br/>2 Examples of Efficient Algorithms: Light Tails . . . . . 163<br/>3 Examples of Efficient Algorithms: Heavy Tails . . . . . 173<br/>4 Tail Estimation . . . . . . . . . . . . . . . . . . . . . . 178<br/>5 Conditioned Limit Theorems . . . . . . . . . . . . . . . 183<br/>6 Large-Deviations or Optimal-Path Approach . . . . . . 187<br/>7 Markov Chains and the h-Transform . . . . . . . . . . 190<br/>8 Adaptive Importance Sampling via the Cross-Entropy<br/>Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 195<br/>9 Multilevel Splitting . . . . . . . . . . . . . . . . . . . . 201<br/>VII Derivative Estimation 206<br/>1 Finite Differences . . . . . . . . . . . . . . . . . . . . . 209<br/>2 Infinitesimal Perturbation Analysis . . . . . . . . . . . 214<br/>x Contents<br/>3 The Likelihood Ratio Method: Basic Theory . . . . . . 220<br/>4 The Likelihood Ratio Method: Stochastic Processes . . 224<br/>5 Examples and SpecialMethods . . . . . . . . . . . . . 231<br/>VIII Stochastic Optimization 242<br/>1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 242<br/>2 Stochastic Approximation Algorithms . . . . . . . . . . 243<br/>3 ConvergenceAnalysis . . . . . . . . . . . . . . . . . . . 245<br/>4 Polyak–RuppertAveraging . . . . . . . . . . . . . . . . 250<br/>5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 253<br/>Part B: Algorithms for Special Models 259<br/>IX Numerical Integration 260<br/>1 Numerical Integration in One Dimension . . . . . . . . 260<br/>2 Numerical Integration in Higher Dimensions . . . . . . 263<br/>3 Quasi-Monte Carlo Integration . . . . . . . . . . . . . . 265<br/>X Stochastic Differential Equations 274<br/>1 Generalities about Stochastic Process Simulation . . . 274<br/>2 BrownianMotion . . . . . . . . . . . . . . . . . . . . . 276<br/>3 The Euler Scheme for SDEs . . . . . . . . . . . . . . . 280<br/>4 The Milstein and Other Higher-Order Schemes . . . . . 287<br/>5 ConvergenceOrders for SDEs: Proofs . . . . . . . . . . 292<br/>6 Approximate Error Distributions for SDEs . . . . . . . 298<br/>7 Multidimensional SDEs . . . . . . . . . . . . . . . . . . 300<br/>8 Reflected Diffusions . . . . . . . . . . . . . . . . . . . . 301<br/>XI Gaussian Processes 306<br/>1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 306<br/>2 Cholesky Factorization. Prediction . . . . . . . . . . . 311<br/>3 Circulant-Embeddings . . . . . . . . . . . . . . . . . . 314<br/>4 Spectral Simulation. FFT . . . . . . . . . . . . . . . . 316<br/>5 Further Algorithms . . . . . . . . . . . . . . . . . . . . 320<br/>6 Fractional BrownianMotion . . . . . . . . . . . . . . . 321<br/>XII Lévy Processes 325<br/>1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 325<br/>2 First Remarks on Simulation . . . . . . . . . . . . . . . 331<br/>3 Dealing with the Small Jumps . . . . . . . . . . . . . . 334<br/>4 Series Representations . . . . . . . . . . . . . . . . . . 338<br/>5 Subordination . . . . . . . . . . . . . . . . . . . . . . . 343<br/>6 Variance Reduction . . . . . . . . . . . . . . . . . . . . 344<br/>7 TheMultidimensional Case . . . . . . . . . . . . . . . 346<br/>8 Lévy-Driven SDEs . . . . . . . . . . . . . . . . . . . . . 348<br/>Contents xi<br/>XIII Markov Chain Monte Carlo Methods 350<br/>1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 350<br/>2 Application Areas . . . . . . . . . . . . . . . . . . . . . 352<br/>3 The Metropolis–Hastings Algorithm . . . . . . . . . . . 361<br/>4 Special Samplers . . . . . . . . . . . . . . . . . . . . . 367<br/>5 The Gibbs Sampler . . . . . . . . . . . . . . . . . . . . 375<br/>XIV Selected Topics and Extended Examples 381<br/>1 Randomized Algorithms for Deterministic Optimization 381<br/>2 Resampling and Particle Filtering . . . . . . . . . . . . 385<br/>3 Counting andMeasuring . . . . . . . . . . . . . . . . . 391<br/>4 MCMC for the Ising Model and Square Ice . . . . . . . 395<br/>5 Exponential Change of Measure in Markov-Modulated<br/>Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 403<br/>6 Further Examples of Change of Measure . . . . . . . . 407<br/>7 Black-BoxAlgorithms . . . . . . . . . . . . . . . . . . . 416<br/>8 Perfect Sampling of Regenerative Processes . . . . . . . 420<br/>9 Parallel Simulation . . . . . . . . . . . . . . . . . . . . 424<br/>10 Branching Processes . . . . . . . . . . . . . . . . . . . 426<br/>11 Importance Sampling for Portfolio VaR . . . . . . . . . 432<br/>12 Importance Sampling for Dependability Models . . . . 435<br/>13 Special Algorithms for the GI/G/1 Queue . . . . . . . 437<br/>Appendix 442<br/>A1 Standard Distributions . . . . . . . . . . . . . . . . . . 442<br/>A2 Some Central Limit Theory . . . . . . . . . . . . . . . 444<br/>A3 FFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444<br/>A4 The EMAlgorithm . . . . . . . . . . . . . . . . . . . . 445<br/>A5 Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . 447<br/>A6 It&ocirc;’s Formula . . . . . . . . . . . . . . . . . . . . . . . 448<br/>A7 Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . 450<br/>A8 Integral Formulas . . . . . . . . . . . . . . . . . . . . . 450<br/>Bibliography 452<br/>Web Links 469<br/>Index 471</p></div><p></p><p><br/></p><br/>