Abstract
LetG be a Lie group ofd×d matrices and ζ be theLLie algebra ofG. We choose some Euclidean norm on ζ, and an orthonormal basis (D1,...Dm) relative to it. Let\(\tilde D_1 ,...,\tilde D_m \) be the corresponding left invariant vector fields onG. In this paper we derive an integration by parts formula for aG-valued Brownian motion corresponding to the “Laplacian”\(\sum _1^m \tilde D_i^2 \).
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