Stochastic algebraic de Rham complexes
type: Item
instance of: scholarly article
title: Stochastic algebraic de Rham complexes
zbMATH Open document ID: 1039.58031
published in: Acta Applicandae Mathematicae
publication date: 2004-01-05T00:00:00Z
review text: In this very interesting paper the author continues his study of extension of the de Rham complexes for finite dimensional compact manifolds \(M\) to the infinite dimensional manifolds -- the loop spaces associated to such manifolds. The work is an interplay between the topological properties of such manifolds and the stochastic properties associated with Brownian motion on such manifolds and their infinite dimensional loop spaces. The work addresses the issue of correct extension of the de Rham cohomology known for finite dimensional manifolds to the associated infinite dimensional manifolds using methods of stochastic analysis based on Malliavin calculus. Partial success in resolving this issue constitutes the essence of this work
reviewed by: Arkady L. Kholodenko
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 57R55
Mathematics Subject Classification ID: 60H07
zbMATH DE Number: 2021276
zbMATH Keywords: algebraic de Rham complex
zbMATH Keywords: Malliavin calculus
zbMATH Keywords: stochastic Chen-Soriau calculus
author: Rémi Léandre
MaRDI profile type: Publication
full work available at URL: b:acap.0000003885.89851.c0
OpenAlex ID: W2022807442
DOI: 10.1023/B:ACAP.0000003885.89851.C0
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description: scientific article; zbMATH DE number 2021276