Preface |
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ix | |
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1 | (4) |
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3 | (2) |
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2 Elements of probability |
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5 | (34) |
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2.1 Sample space and events |
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5 | (1) |
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2.2 Axioms of probability |
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5 | (1) |
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2.3 Conditional probability and independence |
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6 | (3) |
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9 | (2) |
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11 | (2) |
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13 | (2) |
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2.7 Chebyshev's inequality and the laws of large numbers |
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15 | (2) |
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2.8 Some discrete random variables |
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17 | (6) |
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2.9 Continuous random variables |
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23 | (7) |
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2.10 Conditional expectation and conditional variance |
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30 | (9) |
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32 | (5) |
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37 | (2) |
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39 | (8) |
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39 | (1) |
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3.1 Pseudorandom number generation |
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39 | (1) |
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3.2 Using random numbers to evaluate integrals |
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40 | (7) |
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44 | (1) |
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45 | (2) |
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4 Generating discrete random variables |
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47 | (22) |
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4.1 The inverse transform method |
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47 | (6) |
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4.2 Generating a Poisson random variable |
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53 | (1) |
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4.3 Generating binomial random variables |
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54 | (1) |
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4.4 The acceptance--rejection technique |
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55 | (2) |
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4.5 The composition approach |
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57 | (2) |
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4.6 The alias method for generating discrete random variables |
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59 | (3) |
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4.7 Generating random vectors |
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62 | (7) |
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63 | (6) |
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5 Generating continuous random variables |
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69 | (30) |
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69 | (1) |
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5.1 The inverse transform algorithm |
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69 | (4) |
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73 | (9) |
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5.3 The polar method for generating normal random variables |
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82 | (4) |
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5.4 Generating a Poisson process |
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86 | (1) |
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5.5 Generating a nonhomogeneous Poisson process |
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87 | (3) |
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5.6 Simulating a two-dimensional Poisson process |
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90 | (9) |
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94 | (3) |
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97 | (2) |
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6 The multivariate normal distribution and copulas |
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99 | (12) |
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99 | (1) |
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6.1 The multivariate normal |
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99 | (2) |
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6.2 Generating a multivariate normal random vector |
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101 | (3) |
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104 | (5) |
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6.4 Generating variables from copula models |
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109 | (2) |
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109 | (2) |
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7 The discrete event simulation approach |
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111 | (22) |
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111 | (1) |
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7.1 Simulation via discrete events |
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111 | (1) |
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7.2 A single-server queueing system |
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112 | (3) |
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7.3 A queueing system with two servers in series |
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115 | (1) |
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7.4 A queueing system with two parallel servers |
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116 | (3) |
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119 | (1) |
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7.6 An insurance risk model |
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120 | (2) |
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122 | (2) |
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7.8 Exercising a stock option |
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124 | (2) |
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7.9 Verification of the simulation model |
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126 | (7) |
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127 | (3) |
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130 | (3) |
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8 Statistical analysis of simulated data |
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133 | (18) |
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133 | (1) |
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8.1 The sample mean and sample variance |
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133 | (5) |
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8.2 Interval estimates of a population mean |
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138 | (3) |
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8.3 The bootstrapping technique for estimating mean square errors |
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141 | (10) |
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147 | (2) |
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149 | (2) |
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9 Variance reduction techniques |
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151 | (78) |
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151 | (2) |
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9.1 The use of antithetic variables |
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153 | (7) |
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9.2 The use of control variates |
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160 | (6) |
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9.3 Variance reduction by conditioning |
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166 | (14) |
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180 | (10) |
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9.5 Applications of stratified sampling |
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190 | (9) |
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199 | (13) |
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9.7 Using common random numbers |
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212 | (1) |
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9.8 Evaluating an exotic option |
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213 | (4) |
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9.9 Appendix: Verification of antithetic variable approach when estimating the expected value of monotone functions |
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217 | (12) |
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219 | (8) |
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227 | (2) |
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10 Additional variance reduction techniques |
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229 | (26) |
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229 | (1) |
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10.1 The conditional Bernoulli sampling method |
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229 | (4) |
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10.2 A simulation estimator based on an identity of Chen--Stein |
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233 | (8) |
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10.3 Using random hazards |
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241 | (5) |
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10.4 Normalized importance sampling |
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246 | (4) |
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10.5 Latin hypercube sampling |
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250 | (5) |
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252 | (3) |
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11 Statistical validation techniques |
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255 | (24) |
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255 | (1) |
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11.1 Goodness of fit tests |
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255 | (7) |
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11.2 Goodness of fit tests when some parameters are unspecified |
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262 | (3) |
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11.3 The two-sample problem |
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265 | (6) |
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11.4 Validating the assumption of a nonhomogeneous Poisson process |
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271 | (8) |
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275 | (2) |
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277 | (2) |
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12 Markov chain Monte Carlo methods |
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279 | (32) |
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279 | (1) |
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279 | (3) |
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12.2 The Hastings--Metropolis algorithm |
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282 | (2) |
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284 | (10) |
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12.4 Continuous time Markov chains and a queueing loss model |
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294 | (4) |
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298 | (2) |
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12.6 The sampling importance resampling algorithm |
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300 | (4) |
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12.7 Coupling from the past |
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304 | (7) |
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306 | (2) |
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308 | (3) |
Index |
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