Exponential rate of convergence of maximum likelihood estimators for inhomogeneous Wiener processes

The distribution of an inhomogeneous Wiener process is determined by the mean function m(t) ss EW(t) and the variance function b(t) = V^(W(t)) which depend on unknown parameter d _ 0 . Observations are assumed to be in discrete time points where the sample size tends to infinity. Using the general theory of Ibragimow, Hasminskij [2] sufficient conditions for consistency of MLE i?n are established. Exponential bounds for P(\-dn — t?| > e) are given and applied to prove strong consistency of ^n-