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June 1999 A note on limit theorems for multivariate martingales
Uwe Küchler, Michael Sørensen
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Bernoulli 5(3): 483-493 (June 1999).


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 multidimensional 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 occurring in connection with statistical inference for stochastic delay equations.


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Uwe Küchler. Michael Sørensen. "A note on limit theorems for multivariate martingales." Bernoulli 5 (3) 483 - 493, June 1999.


Published: June 1999
First available in Project Euclid: 27 February 2007

zbMATH: 0943.60016
MathSciNet: MR1693604

Keywords: central limit theorem , likelihood inference , multivariate Gaussian diffusions , stochastic delay equations , Weak law of large numbers

Rights: Copyright © 1999 Bernoulli Society for Mathematical Statistics and Probability


Vol.5 • No. 3 • June 1999
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