Geodesic
Stochastic parallel transport and connections of $H^2M$
Archivum mathematicum, Tome 35 (1999) no. 4, pp. 305-315.

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In this paper we prove that there is a bijective correspondence between connections of $H^2M$, 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 $H^2M$. We interpret such prolongation in terms of stochastic calculus.
Classification : 53B15, 53C05, 58J65
Keywords: second order geometry; stochastic calculus; connections; parallel transport 
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     author = {Catuogno, Pedro},
     title = {Stochastic parallel transport and connections of $H^2M$},
     journal = {Archivum mathematicum},
     pages = {305--315},
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     zbl = {1049.58035},
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     url = {http://geodesic.mathdoc.fr/item/ARM_1999__35_4_a2/}
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Catuogno, Pedro. Stochastic parallel transport and connections of $H^2M$. Archivum mathematicum, Tome 35 (1999) no. 4, pp. 305-315. http://geodesic.mathdoc.fr/item/ARM_1999__35_4_a2/