Bernoulli

  • Bernoulli
  • Volume 5, Number 3 (1999), 483-493.

A note on limit theorems for multivariate martingales

Uwe Küchler and Michael Sørensen

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Abstract

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.

Article information

Source
Bernoulli, Volume 5, Number 3 (1999), 483-493.

Dates
First available in Project Euclid: 27 February 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1172617200

Mathematical Reviews number (MathSciNet)
MR1693604

Zentralblatt MATH identifier
0943.60016

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

Citation

Küchler, Uwe; Sørensen, Michael. A note on limit theorems for multivariate martingales. Bernoulli 5 (1999), no. 3, 483--493. https://projecteuclid.org/euclid.bj/1172617200


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