Probability structure preserving and absolute continuity
type: Item
instance of: scholarly article
title: Probability structure preserving and absolute continuity
zbMATH Open document ID: 1002.60046
DOI: 10.1016/S0246-0203(01)01104-9
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 2002-08-19T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77725
review text: The probability structure preserving mapping (PSPM) in the sense that \( V(F+G)= V(F)+V(G), V(FG)= V(F)V(G), E[F] = {\tilde E}[V(F)]\) for all elements \(F\) and \(G\) of the space \(\varepsilon\) of finite linear combinations of the exponential functionals defined from an abstract Wiener space together with the corresponding expectation \(E\) (respectively, \(V(F) \in \tilde {\varepsilon}\) with \( \tilde E\)) is introduced similarly to a correspondence introduced in a previous article of the author and \textit{P. A. Meyer} [in: Stochastic processes, 141-147 (1993; Zbl 0798.60057)] but a similar role is played by multiple Itô type integrals. A particular PSPM between Brownian motion and fractional Brownian motion (FBM) with Hurst parameter \(H\) is established to define stochastic integral for FBM and to prove a Girsanov type theorem on absolute continuity for FBM.
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60B11
Mathematics Subject Classification ID: 28B20
Mathematics Subject Classification ID: 60H07
zbMATH DE Number: 1783425
zbMATH Keywords: stochastic integral
zbMATH Keywords: probability structure preserving mapping
zbMATH Keywords: absolute continuity
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: Radon-Nikodym derivative
zbMATH Keywords: anticipative Girsanov theorem
author: Yaozhong Hu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1783425