10.18452/3737
Küchler, Uwe
Sørensen, Michael
A Note on Limit Theorems for Multivariate Martingales
Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät
2006
stochastic delay equations
Central limit theorem
multivariate Gaussian diffusions
likelihood inference
weak law of large numbers
330 Wirtschaft
17 Wirtschaft
Humboldt-Universität zu Berlin
Humboldt-Universität zu Berlin
2017-06-15
2017-06-15
2006-02-02
2006-02-02
http://edoc.hu-berlin.de/series/sfb-373-papers/1998-45/PDF/45.pdf
http://edoc.hu-berlin.de/18452/4389
urn:nbn:de:kobv:11-10056985
Multivariate versions of the law of large numbers and the central limit theorem for martingales are given in a generality that is often necessary when studying statistical inference for stochastic process models. To illustrate the usefulness of the results, we consider estimation for a multi-dimensional Gaussian diffusion, 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 different nature, which are typical of the problems occuring in connection with statistical inference for stochastic delay equations.