Rates of convergence of strongly consistent parameter estimates in
diffusion processes are studied via large deviations (LD) laws for the
suprema of the estimation error's tail processes. Such measures of
convergence rates are considerably stronger than the widely used
central limit theorems. First, * conditional* LD limits are
obtained in an indirect way, by utilizing a general martingale
law. Those are then applied to derive simple stopping rules which have
direct practical significance.

D. Levanony

Mon Nov 13 10:43:02 EST 1995