Explicit stochastic analysis of Brownian motion and point measures on Riemannian manifolds
type: Item
instance of: scholarly article
title: Explicit stochastic analysis of Brownian motion and point measures on Riemannian manifolds
zbMATH Open document ID: 0940.58023
author: Jean-Jacques Prat
author: Nicolas Privault
published in: Journal of Functional Analysis
publication date: 2000-07-17T00:00:00Z
review text: The authors study the three types of gradient operators of stochastic analysis on Riemannian manifolds in the Gaussian measure setting [see also \textit{S. Fang} and \textit{P. Malliavin}, J. Funct. Anal. 118, No. 1, 249-274 (1993; Zbl 0798.58080)] and in the Poisson measure setting. They obtain explicit formulas linking the gradients by explicit calculations using the Fock gradient and divergence of the flat case. Their method shows that the difficulties of stochastic calculus on manifolds are similar to those of the Poisson case. The anticipating integral on manifolds is also treated [see also \textit{S. Fang}, J. Funct. Anal. 131, No. 1, 228-253 (1995; Zbl 0847.58081)].
reviewed by: Mihai Gradinaru
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 1346907
zbMATH Keywords: stochastic calculus of variations
zbMATH Keywords: Brownian motion
zbMATH Keywords: random measures
zbMATH Keywords: Riemannian manifolds
MaRDI profile type: Publication
OpenAlex ID: W1970998421
cites work: Analysis and geometry on configuration spaces
cites work: A quantum nonadapted Ito formula and stochastic analysis in Fock scale
cites work: Q3996311
cites work: Calcul des variations stochastique et processus de sauts
cites work: Large deviations and the Malliavin calculus
cites work: Q4735879
cites work: Renormalized differential geometry on path space: Structural equation, curvature
cites work: Stochastic anticipative integrals on a Riemannian manifold
cites work: Stochastic anticipative calculus on the path space over a compact Riemannian manifold
cites work: Stochastic analysis on the path space of a Riemannian manifold. I: Markovian stochastic calculus
cites work: L'intégrale stochastique comme opérateur de divergence dans l'espace fonctionnel
cites work: Q4337939
cites work: Q4842684
cites work: Stochastic calculus with anticipating integrands
cites work: Chaotic and variational calculus in discrete and continuous time for the poisson process
cites work: An introduction to analysis on Wiener space
DOI: 10.1006/JFAN.1999.3440
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description: scientific article; zbMATH DE number 1346907