Quasi sure quadratic variation of smooth martingales
type: Item
instance of: scholarly article
title: Quasi sure quadratic variation of smooth martingales
zbMATH Open document ID: 0804.60047
published in: Journal of Mathematics of Kyoto University
publication date: 1994-10-13T00:00:00Z
review text: We prove that the quadratic variation process of a smooth martingale \({\mathbf M}= \{M_ t\}\) in the sense of Malliavin-Nualart can be constructed as the quasi-sure limit of sums of the form \(\sum M(\Delta_ i)\), as the size of the subdivision \(\Delta\) goes to zero. Then this result is extended to the case of smooth semimartingales and two- parameter strong smooth martingales. A recent work of \textit{Z. Liang} (preprint) shows that the same result holds true for two-parameter (not necessarily strong) smooth martingales.
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60G44
zbMATH DE Number: 633569
zbMATH Keywords: quadratic variation process of a smooth martingale
zbMATH Keywords: two-parameter strong smooth martingales
author: Jiagang Ren
reviewed by: Jingli Ren
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519068
OpenAlex ID: W1501033630
DOI: 10.1215/KJM/1250519068
description: scientific article; zbMATH DE number 633569