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Ruffino","submitted_at":"2015-04-24T16:42:45Z","abstract_excerpt":"Consider a manifold $M$ endowed locally with a pair of complementary distributions $\\Delta^H \\oplus \\Delta^V=TM$ and let $\\text{Diff}(\\Delta^H, M)$ and $\\text{Diff}(\\Delta^V, M)$ be the corresponding Lie subgroups generated by vector fields in the corresponding distributions. We decompose a stochastic flow with jumps, up to a stopping time, as $\\varphi_t = \\xi_t \\circ \\psi_t$, where $\\xi_t \\in \\text{Diff}(\\Delta^H, M)$ and $\\psi_t \\in \\text{Diff}(\\Delta^V, M)$. 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