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Zbl 1039.58031
Léandre, Rémi
Stochastic algebraic de Rham complexes. (English)
[J] Acta Appl. Math. 79, No. 3, 217-247 (2003). ISSN 0167-8019; ISSN 1572-9036/e

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
[Arkady L. Kholodenko (Clemson)]

MSC 2000:: *58J65 Diffusion processes and stochastic analysis on manifolds
57R55 Differentiable structures
60H07 Stochastic calculus of variations and the Malliavin calculus

Keywords: algebraic de Rham complex; Malliavin calculus; stochastic Chen-Soriau calculus

Cited in: Zbl 1061.58033

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