Abstract:

The distribution of an inhomogeneous Wiener process is determined by the mean function $m(t)=E W(t)$ and the variance function $b(t) = V(W(t))$ which depend on unknown parameter $\vartheta\in\Theta$. Observations are assumed to be in discrete time points where the sample size tends to infinity. Using the general theory of Ibragimow, Hasminskij, sufficient conditions for consistency of MLE $\hat{\vartheta}_n$ are established. Exponential bounds for $P(\vert \hat{\vartheta}_n-\vartheta\vert >\varepsilon)$ are given and applied to prove strong consistency of $\hat{\vartheta}_n$.