GENERATION OF RANDOM VARIATES USING ASYMPTOTIC EXPANSIONS

Monte-Carlo methods are widely used numerical tools in various fields of application, like rarefied gas dynamics, vacuum technology, stellar dynamics or nuclear physics. A central part is the generation of rand om variates according to a given probability law. Fundamental techniqu es are the inversion principle or the acceptance-rejection method - bo th may be quite time-consuming if the given probability law has a comp licated structure. In this paper probability laws depending on a small parameter are considered and the use of asymptotic expansions to gene rate random variates is investigated. The results given in the paper a re restricted to first order expansions. Error estimates for the discr epancy as well as for the bounded Lipschitz distance of the asymptotic expansion are derived. Furthermore the integration error for some spe cial classes of functions is given. The efficiency of the method is pr oved by a numerical example from rarefied gas flows.