A note on limit theorems for multivariate martingales
type: Item
instance of: scholarly article
title: A note on limit theorems for multivariate martingales
zbMATH Open document ID: 0943.60016
DOI: 10.2307/3318713
author: Uwe Küchler
author: Michael Sørensen
published in: Bernoulli
publication date: 2000-09-04T00:00:00Z
full work available at URL: http://edoc.hu-berlin.de/18452/4389
review text: The main result is a central limit theorem for multivariate martingales under relatively mild assumptions. As a corollary, a weak law of large numbers is established under the same conditions. The hypotheses are sufficiently general as to allow these results to be applied in situations where previous theorems of this type cannot. As examples, the authors use the CLT to discern the asymptotic distribution of the maximum-likelihood estimator in Gaussian diffusion models and to make statistical inferences about the solutions of stochastic delay equations. Similarly, the weak law is used to study the consistency of least-squares estimators in certain semi-martingale models.
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 1334559
zbMATH Keywords: central limit theorem
zbMATH Keywords: weak law of large numbers
zbMATH Keywords: multivariate martingales
zbMATH Keywords: maximum likelihood
zbMATH Keywords: stochastic delay equations
zbMATH Keywords: semi-martingales
zbMATH Keywords: Gaussian diffusions
reviewed by: R. James Tomkins
MaRDI profile type: Publication
OpenAlex ID: W1966060936
description: scientific article; zbMATH DE number 1334559