Rates of convergence in the functional CLT for multidimensional continuous time martingales.
type: Item
instance of: scholarly article
title: Rates of convergence in the functional CLT for multidimensional continuous time martingales.
zbMATH Open document ID: 1047.60026
DOI: 10.1016/S0304-4149(00)00054-5
author: B. Courbot
published in: Stochastic Processes and their Applications
publication date: 2004-09-22T00:00:00Z
review text: A speed of convergence in the multidimensional functional CLT for martingales can be measured by means of the Prokhorov's distance between a Brownian motion and the martingale. Assuming square integrability the paper presents an estimation of that distance. The estimate contains uniform Ky Fan's distance between quadratic variation of the considered martingale and the variance of Brownian bridge, and the influence of jumps measured by their uniform Ky Fan's distance from zero process, only. The last section of the paper compares the reached result with known results.
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60G44
zbMATH DE Number: 2102361
zbMATH Keywords: multidimensional martingale
zbMATH Keywords: multidimensional Brownian motion
zbMATH Keywords: Prokhorov's distance
zbMATH Keywords: Ky Fan's distance
zbMATH Keywords: uniform Ky Fan's distance
zbMATH Keywords: quadratic covariation of two square integrable martingales
zbMATH Keywords: quadratic variation of a square integrable martingale
reviewed by: Petr Lachout
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2102361