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Stochastic Algebraic de Rham Complexes

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Abstract

We define completion of the algebraic de Rham complex associated to the algebras of functionals smooth in the Chen–Souriau sense or in the Nualart–Pardoux sense over the loop space. We show that the stochastic algebraic de Rham cohomology groups are equal to the deterministic cohomology groups of the loop space.

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Authors and Affiliations

  1. Institut Elie Cartan, Département de Mathématiques, Université de Nancy I, 54500, Vandoeuvre-les-Nancy, France

    Rémi Léandre

  2. Faculdad de Matematica, Universidad Catolica de Chile, Casilla 306, Santiago 22, Chile

    Rémi Léandre

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Léandre, R. Stochastic Algebraic de Rham Complexes. Acta Applicandae Mathematicae 79, 217–247 (2003). https://doi.org/10.1023/B:ACAP.0000003885.89851.c0

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