Unfolding the Skorohod reflection of a semimartingale
type: Item
instance of: scholarly article
title: Unfolding the Skorohod reflection of a semimartingale
zbMATH Open document ID: 1172.60012
author: Vilmos Prokaj
published in: Statistics \& Probability Letters
publication date: 2009-03-02T00:00:00Z
review text: Let\(\;(U_{t})_{t\geq 0}\) be a continuous semimartingale with \(U_{0}=0,\) and \( Y_{t}=U_{t}+\sup_{s\leq t}(-U_{s}),\;t\geq 0\), the Skorohod reflection of \(U\). It is proved that on a suitable probability space there exists a continuous semimartingale \((Y_{t}^{\prime })_{t\geq 0}\;\)such\ that \(\left| Y_{t}^{\prime }\right| =Y_{t}\) and \(dY_{t}^{\prime }=\;\)sgn\( \;(Y_{t}^{\prime })dU_{t},\;t\geq 0\), This generalizes the well-known fact that the Skorohod reflection of a Wiener process is the absolute value of another Wiener process with finer filtration.
reviewed by: Marius Iosifescu
Mathematics Subject Classification ID: 60G48
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 5522235
zbMATH Keywords: semimartingale
zbMATH Keywords: Wiener process
zbMATH Keywords: Skorohod reflection
MaRDI profile type: Publication
full work available at URL: j.spl.2008.09.029
OpenAlex ID: W2046595289
cites work: Q4303982
DOI: 10.1016/J.SPL.2008.09.029
description: scientific article; zbMATH DE number 5522235