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Some guildelines and guarantees for common random numbers. (English) Zbl 0758.65091

Common random numbers (CRN) is a broadly used technique for reducing variance in comparing stochastic systems. In the comparison the estimation of \(E[f(X)-g(Y)]\) is required. \(f\) and \(g\) are real valued cost or performance functions. CRN is used in order to minimize \[ \text{Var}[f(X)-g(Y)]=\text{Var}[f(X)]+\text{Var}[g(Y)]- 2\text{Cov}[f(X),g(Y) ] \] i.e. to maximize Cov. The paper develops the theory of CRN. The results of the theory allow to specify new classes of models and/or comparisons for which CRN is provable beneficial. The results are consistent with simulation practice (and folklore).
The study is based on the timing events rather than sequences of states of discrete events. The paper deals with the three variants of applications of CRN: Distribution comparisons, structural comparisons and sensitivity analysis.
Reviewer: J.Král (Praha)

MSC:

65C99 Probabilistic methods, stochastic differential equations
65C10 Random number generation in numerical analysis
62J10 Analysis of variance and covariance (ANOVA)
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