On changing time for two-parameter strong martingales: A counterexample
type: Item
instance of: scholarly article
title: On changing time for two-parameter strong martingales: A counterexample
zbMATH Open document ID: 0596.60047
author: P. Imkeller
published in: The Annals of Probability
publication date: 1986-01-01T00:00:00Z
review text: Brownian motion owes part of its significance to the fact that any continuous martingale may be considered as a Brownian motion running with a different clock. This means that by a suitable time change any continuous martingale can be transformed into Brownian motion. Since its multiparameter analogue, the Wiener sheet, is a strong martingale and the strong martingale property is preserved under transformations by stopping domains, it could only be expected to play a similarly central role among strong martingales. In this paper a strong martingale is constructed which is measurable w.r.t. the Wiener sheet's filtration, but allows no transformation into the Wiener sheet by changing time with stopping domains.
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 3960679
zbMATH Keywords: two-parameter strong martingales
zbMATH Keywords: Wiener sheet
zbMATH Keywords: strong martingale property
zbMATH Keywords: Wiener sheet's filtration
zbMATH Keywords: changing time
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992462
OpenAlex ID: W2075067085
Wikidata QID: Q125055080
DOI: 10.1214/AOP/1176992462
description: scientific article; zbMATH DE number 3960679