On the Malliavin calculus for SDE's on Hilbert spaces
type: Item
instance of: scholarly article
title: On the Malliavin calculus for SDE's on Hilbert spaces
zbMATH Open document ID: 1034.60059
DOI: 10.1023/A:1025741617744
author: Takashi Komatsu
published in: Acta Applicandae Mathematicae
publication date: 2003-12-09T00:00:00Z
review text: A stochastic system \(x^u(t)\) of particles indexed by \(u\in R^d\) is modelled by a stochastic differential equation (SDE) on a Hilbert space. If \(\pi\) is an \(R^M\)-valued bounded linear mapping on this space, the Malliavin calculus is applied to get a condition (called a `partial Hörmander condition') under which \(\pi(x(T))\) has a smooth density with respect to the Lebesgue measure of \(R^M\). Then the propagation of the absolute continuity of measures on \(R^d\) by the stochastic flow of the SDE is studied.
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60J75
zbMATH DE Number: 2015163
zbMATH Keywords: stochastic flow
zbMATH Keywords: Malliavin calculus
zbMATH Keywords: Hörmander condition
reviewed by: Jean Picard
MaRDI profile type: Publication
full work available at URL: a:1025741617744
OpenAlex ID: W62348164
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description: scientific article; zbMATH DE number 2015163