Stochastic parallel transport and connections of H 2 M

Pedro Catuogno

Archivum Mathematicum (1999)

  • Volume: 035, Issue: 4, page 305-315
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Catuogno, Pedro. "Stochastic parallel transport and connections of $H^2M$." Archivum Mathematicum 035.4 (1999): 305-315. <http://eudml.org/doc/248363>.

@article{Catuogno1999,
abstract = {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.},
author = {Catuogno, Pedro},
journal = {Archivum Mathematicum},
keywords = {second order geometry; stochastic calculus; connections; parallel transport; second order frame bundle; stochastic calculus; connection; parallel transport},
language = {eng},
number = {4},
pages = {305-315},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Stochastic parallel transport and connections of $H^2M$},
url = {http://eudml.org/doc/248363},
volume = {035},
year = {1999},
}

TY - JOUR
AU - Catuogno, Pedro
TI - Stochastic parallel transport and connections of $H^2M$
JO - Archivum Mathematicum
PY - 1999
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 035
IS - 4
SP - 305
EP - 315
AB - 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.
LA - eng
KW - second order geometry; stochastic calculus; connections; parallel transport; second order frame bundle; stochastic calculus; connection; parallel transport
UR - http://eudml.org/doc/248363
ER -

References

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  10. Kobayashi S., Canonical Forms on Frame Bundles of Higher Order Contact, Proc. Symp. Pure Math. 3, 186–193, 1961. (193,) MR0126810
  11. Kobayashi S., Nomizu K., Foundations of Differential Geometry, Interscience, 1 (1963), 2 (1968). (1963) Zbl0119.37502MR0152974
  12. Kolář I., On some Operations with Connections, Math. Nachr. 69, 297–306, 1975. (1975) Zbl0318.53034MR0391157
  13. Meyer P. A., Géométrie Différentielle Stochastique, Séminaire de Probabilités XV. Lecture Notes in Mathematics 851, Springer 1981. (1981) 
  14. Meyer P. A., Géométrie Différentielle Stochastique (bis), Séminaire de Probabilités XVI. Lecture Notes in Mathematics 921, Springer 1982. (1982) Zbl0539.58039MR0658725
  15. Schwartz L., Géométrie Différentielle du 2 e ordre, Semimartingales et Équations Différentielle Stochastiques sur une Variété Différentielle, Séminaire de Probabilités XVI. Lecture Notes in Mathematics 921, Springer 1982. (1982) MR0658722
  16. Shigekawa I., On Stochastic Horizontal Lifts, Z. Wahrscheinlichkeitsheorie verw. Geviete 59, 211–221, 1982. (1982) Zbl0487.60056MR0650613

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