Malliavin calculus for white noise driven parabolic SPDEs
type: Item
instance of: scholarly article
title: Malliavin calculus for white noise driven parabolic SPDEs
zbMATH Open document ID: 0928.60040
DOI: 10.1023/A:1008686922032
author: Vlad Bally
author: Etienne Pardoux
published in: Potential Analysis
publication date: 2000-01-02T00:00:00Z
review text: For an SPDE of the form \(\partial_t X=\partial^2_t X+\psi(X)+\varphi(X)\dot{W}\) with space time white noise \(W(t,x)\), \(x\in[0,1]\), and the Neumann boundary condition, the authors use the Malliavin calculus to prove that the law of \((X(t,x_1),\ldots,X(t,x_d))\), \(0\leq x_1<\ldots<x_d\), is absolutely continuous with respect to Lebesgue measure with strictly positive density, provided the coefficients \(\psi\), \(\varphi\) are infinitely differentiable with bounded derivatives of all orders.
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 35R60
zbMATH DE Number: 1241116
zbMATH Keywords: stochastic partial differential equations
zbMATH Keywords: Malliavin calculus
zbMATH Keywords: space-time white noise
reviewed by: Marek Capiński
MaRDI profile type: Publication
full work available at URL: a:1008686922032
OpenAlex ID: W141349636
description: scientific article; zbMATH DE number 1241116