A Note on Limit Theorems for Multivariate Martingales

Multivariate versions of the law of large numbers and the cen tral limit theorem for martingales are given in a generality that is often necessary when studying statistical inference for stochastic pro cess models To illustrate the usefulness of the results we consider estimation for a multidimensional Gaussian diusion where results on consistency and asymptotic normality of the maximum likelihood estimator are obtained in cases that were not covered by previously published limit theorems The results are also applied to martingales of a dierent nature which are typical of the problems occuring in connection with statistical inference for stochastic delay equations Key words Central limit theorem multivariate Gaussian diusions likelihood inference stochastic delay equations weak law of large num bers Research for this paper was partially carried out within Sonderforschungsbereic