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Special Itô maps and an $L^2$ Hodge theory for one forms on path spaces
Published 21 Nov 2019 in math.PR | (1911.09618v1)
Abstract: We prove a Kodaira-Hodge decomposition on differential 1-forms on the space of non-smooth paths over a Riemannian manifold, allowing us to define the corresponding first cohomology group. This uses the It^o map of a Brownian system and damped stochastic parallel translation.
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