Chaotic Monte Carlo computation: A dynamical effect of random-number generations

Chaotic maps with absolutely continuous invariant probability measures are implemented as random-number generators for Monte Carlo computation. We obs erve that such Monte Carlo computation based on chaotic random-number gener ators yields sometimes unexpected dynamical dependency behavior which canno t be explained by usual statistical arguments. Furthermore, we find that su perefficient Monte Carlo computation with O(1/N-2) mean square error can be carried out as an extreme case of such dynamical dependency behavior. Here , such superefficiency sharply contrasts with the conventional Monte Carlo simulation with O(1/N) mean square error. By deriving a necessary and suffi cient condition for the superefficiency, it is shown that such high-perform ance Monte Carlo simulations can be carried out only if there exists a stro ng correlation with chaotic dynamical variables. Numerical calculation illu strates this dynamics dependency and the superefficiency of various chaotic Monte Carlo computations.