Generation of random variates using asymptotic expansions (Q1377271)

This paper considers the generation of random numbers according to a density \(f(x; \varepsilon)\), which depends on a small parameter \(\varepsilon>0\). The generation is based on the inversion principle but with asymptotic expansions of \(f(x; \varepsilon)\) with respect to the small parameter \(\varepsilon\). After presenting some basic notations concerning asymptotic expansions and measure theory, first-order expansions to generate an \(f\)-distributed pointset are investigated. Theorems on the error estimates for the discrepancy and for the bounded Lipschitz distance of the asymptotic expansions are derived. A numerical example in computational fluid dynamics illustrates the efficiency of the proposed method. (Several typographical errors bothered the reviewer to read the paper).