A conditional approach to the anticipating Girsanov transformation
type: Item
instance of: scholarly article
title: A conditional approach to the anticipating Girsanov transformation
zbMATH Open document ID: 0791.60038
DOI: 10.1007/BF01192167
author: Hans Föllmer
author: Rainer Buckdahn
publication date: 1994-07-07T00:00:00Z
review text: We study the law of a stochastic differential equation \(d\xi_ t=d \omega_ t+k_ t (\xi,\omega)dt\), where the drift anticipates the future behavior of the Brownian path \(\omega\), for example the endpoint. We first investigate anticipation of the endpoint, using a conditional Girsanov transformation and methods of Malliavin calculus. A combination with results of the first author [ibid. 90, No. 2, 223-240 (1991; Zbl 0735.60057)] leads to new versions of the anticipating Girsanov transformation of Ramer and Kusuoka, and in particular to explicit formulas for the Carleman-Fredholm determinant.
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60J45
zbMATH DE Number: 569045
zbMATH Keywords: stochastic differential equation
zbMATH Keywords: anticipation
zbMATH Keywords: conditional Girsanov transformation
zbMATH Keywords: Malliavin calculus
zbMATH Keywords: explicit formulas for the Carleman- Fredholm determinant
reviewed by: Rainer Buckdahn
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 569045