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Stochastic parallel transport and connections of H 2 M

Pedro Catuogno — 1999

Archivum Mathematicum

In this paper we prove that there is a bijective correspondence between connections of H 2 M , the principal bundle of the second order frames of M , and stochastic parallel transport in the tangent space of M . We construct in a direct geometric way a prolongation of connections without torsion of M to connections of H 2 M . We interpret such prolongation in terms of stochastic calculus.

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