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Lectures on Gaussian Approximations with Malliavin Calculus Read chapter Read first chapter

2013 | OriginalPaper | Chapter

A Note on Stochastic Calculus in Vector Bundles

Authors : Pedro J. Catuogno, Diego S. Ledesma, Paulo R. Ruffino

Published in: Séminaire de Probabilités XLV

Publisher: Springer International Publishing

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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.

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previous chapter Malliavin Calculus and Self Normalized Sums
next chapter Functional Co-monotony of Processes with Applications to Peacocks and Barrier Options
Literature
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M. Arnaudon, A. Thalmaier, Horizontal martingales in vector bundles. Séminaire de Probabilités, XXXVI. Lecture Notes in Math., vol. 1801 (Springer, Berlin, 2003), pp. 419–456
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J. Eells, L. Lemaire, Selected topics in harmonic maps. CBMS Regional Conference Series in Mathematics, vol. 50 (American Mathematical Society, Providence, RI, 1983)
5.
M. Emery, Stochastic Calculus in Manifolds. With an appendix by P. A. Meyer. Universitext (Springer, Berlin, 1989)MATHCrossRef
6.
J.R. Norris, A complete differential formalism for stochastic calculus in manifolds. Séminaire de Probabilités, XXVI. Lecture Notes in Math., vol. 1526 (Springer, Berlin, 1992), pp. 189–209
7.
8.
W.A. Poor, Differential Geometric Structures (McGraw-Hill, New York, 1981)MATH
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Y. Xin, Geometry of harmonic maps. Progress in Nonlinear Differential Equations and their Applications, vol. 23 (Birkhäuser Boston, Boston, MA, 1996)
Metadata
Title
A Note on Stochastic Calculus in Vector Bundles
Authors
Pedro J. Catuogno
Diego S. Ledesma
Paulo R. Ruffino
Copyright Year
2013
Publisher
Springer International Publishing
Book
Séminaire de Probabilités XLV

Print ISBN: 978-3-319-00320-7

Electronic ISBN: 978-3-319-00321-4

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-319-00321-4_14