Abstract
The aim of these notes is to relate covariant stochastic integration in a vector bundle E [as in Norris (Séminaire de Probabilités, XXVI, vol. 1526, Springer, Berlin, 1992, pp. 189–209)] with the usual Stratonovich calculus via the connector \(\mathcal{K}_{\nabla }: \mathit{TE} \rightarrow E\) [cf. e.g. Paterson (Canad. J. Math. 27(4):766–791, 1975) or Poor (Differential Geometric Structures, McGraw-Hill, New York, 1981)] which carries the connection dependence.
P. J. Catuogno was partially supported by CNPq, grant no. 302704/2008-6, 480271/2009-7 and FAPESP, grant no. 07/06896-5. D. S. Ledesma was supported by FAPESP, grant no. 10/20347-7. P. R. Ruffino was partially supported by CNPq, grant no. 306264/2009-9, 480271/2009-7 and FAPESP, grant no. 7/06896-5.
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Catuogno, P.J., Ledesma, D.S., Ruffino, P.R. (2013). A Note on Stochastic Calculus in Vector Bundles. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLV. Lecture Notes in Mathematics(), vol 2078. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00321-4_14
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