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Preface | |
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Introduction | |
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Exercises | |
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Elements of Probability | |
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Sample Space and Events | |
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Axioms of Probability | |
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Conditional Probability and Independence | |
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Random Variables | |
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Expectation | |
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Variance | |
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Chebyshev's Inequality and the Laws of Large Numbers | |
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Some Discrete Random Variables | |
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Continuous Random Variables | |
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Conditional Expectation and Conditional Variance | |
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Exercises | |
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Bibliography | |
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Random Numbers | |
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Introduction | |
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Pseudorandom Number Generation | |
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Using Random Numbers to Evaluate Integrals | |
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Exercises | |
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Bibliography | |
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Generating Discrete Random Variables | |
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The Inverse Transform Method | |
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Generating a Poisson Random Variable | |
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Generating Binomial Random Variables | |
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The Acceptance-Rejection Technique | |
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The Composition Approach | |
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The Alias Method for Generating Discrete Random Variables | |
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Generating Random Vectors | |
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Exercises | |
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Generating Continuous Random Variables | |
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Introduction | |
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The Inverse Transform Algorithm | |
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The Rejection Method | |
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The Polar Method for Generating Normal Random Variables | |
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Generating a Poisson Process | |
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Generating a Nonhomogeneous Poisson Process | |
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Simulating a Two-Dimensional Poisson Process | |
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Exercises | |
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Bibliography | |
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The Multivariate Normal Distribution and Copulas | |
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Introduction | |
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The Multivariate Normal | |
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Generating a Multivariate Normal Random Vector | |
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Copulas | |
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Generating Variables from Copula Models | |
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Exercises | |
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The Discrete Event Simulation Approach | |
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Introduction | |
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Simulation via Discrete Events | |
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A Single-Server Queueing System | |
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A Queueing System with Two Servers in Series | |
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A Queueing System with Two Parallel Servers | |
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An Inventory Model | |
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An Insurance Risk Model | |
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A Repair Problem | |
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Exercising a Stock Option | |
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Verification of the Simulation Model | |
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Exercises | |
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Bibliography | |
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Statistical Analysis of Simulated Data | |
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Introduction | |
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The Sample Mean and Sample Variance | |
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Interval Estimates of a Population Mean | |
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The Bootstrapping Technique for Estimating Mean Square Errors | |
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Exercises | |
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Bibliography | |
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Variance Reduction Techniques | |
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Introduction | |
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The Use of Antithetic Variables | |
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The Use of Control Variates | |
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Variance Reduction by Conditioning | |
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Stratified Sampling | |
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Applications of Stratified Sampling | |
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Importance Sampling | |
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Using Common Random Numbers | |
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Evaluating an Exotic Option | |
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Appendix: Verification of Antithetic Variable Approach When Estimating the Expected Value of Monotone Functions | |
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Exercises | |
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Bibliography | |
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Additional Variance Reduction Techniques | |
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Introduction | |
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The Conditional Bernoulli Sampling Method | |
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Normalized Importance Sampling | |
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Latin Hypercube Sampling | |
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Exercises | |
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Statistical Validation Techniques | |
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Introduction | |
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Goodness of Fit Tests | |
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Goodness of Fit Tests When Some Parameters Are Unspecified | |
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The Two-Sample Problem | |
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Validating the Assumption of a Nonhomogeneous Poisson Process | |
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Exercises | |
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Bibliography | |
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Markov Chain Monte Carlo Methods | |
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Introduction | |
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Markov Chains | |
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The Hastings-Metropolis Algorithm | |
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The Gibbs Sampler | |
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Continuous time Markov Chains and a Queueing Loss Model | |
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Simulated Annealing | |
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The Sampling Importance Resampling Algorithm | |
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Coupling from the Past | |
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Exercises | |
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Bibliography | |
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Index | |