An Iterative Monte Carlo Scheme for Generating Lie Group-Valued Random Variables

In this paper a simple approximation scheme is proposed for the problem of generating and computing expectations of functionals of a wide class of random variables with values in a compact Lie group. The algorithm is suggested by the time-discretization of an ergodic diffusion leaving invariant the distribution of interest. It is shown to converge as the discretization step goes to zero with the iterations in a natural way.