Rarefied Gas Dynamics and Monte Carlo Methods.

Abstract : The research supported by this grant was primarily on quasi-random sequences, which are a deterministic alternative to random or pseudo-random sequences', and their use in Monte Carlo methods, These methods are vastly superior to standard Monte Carlo, at least in principle, because the errors are of size O(N-1) rather than the usual O(N-1/).On the other hand, this gain in accuracy can be lost if the domain of integration is of high dimension or the function to be integrated is not smooth. In joint work with Bradley Moskowitz, we succeeded in overcoming these limitations for a number of Monte Carlo methods, including the acceptance-rejection method, Feynman-Kac integrals and diffusion Monte Carlo.