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Approximating Ito integrals of differential forms and geodesic deviation. (English) Zbl 0519.60053


MSC:

60H05 Stochastic integrals
58J65 Diffusion processes and stochastic analysis on manifolds
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References:

[1] Bismut, J. M., Principes de Mécanique Aleatoire, Lecture Note Math. 866 (1981), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0457.60002
[2] Darling, R. W.R., Martingales on manifolds and geometric Ito calculus, Ph.D. Thesis (1982), England: University of Warwick, England · Zbl 0482.58035
[3] Eliasson, H. I., Geometry of manifolds of maps, J. Differential Geometry, I, 169-194 (1967) · Zbl 0163.43901
[4] Ikeda, N.; Watanabe, S., Stochastic differential equations and diffusion processes (1981), Amsterdam: North Holland, Amsterdam · Zbl 0495.60005
[5] Kallianpur, G., Stochastic filtering theory (1980), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0458.60001 · doi:10.1007/978-1-4757-6592-2
[6] Kunita, H., Some extensions of Ito’s formula, Sem. Prob. XV, 118-141 (1981), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0471.60061
[7] Lang, S., Differential manifolds (1972), Reading, Mass: Addison-Wesley, Reading, Mass · Zbl 0239.58001
[8] Metivier, M.; Pellaumail, J., Stochastic integration (1980), New York: Academic Press, New York · Zbl 0463.60004
[9] Meyer, P. A., Géométric stochastique sans larmes, Sem. de Probabilités XV, 41-102 (1980), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York
[10] Schwartz, L., Semi-martingales sur des variétes, et martingales conformes sur des variétés analytiques complexes, Lecture Notes Math. 780 (1980), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0433.60047
[11] Shigekawa, Ichiro, On stochastic horizontal lifts, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 59, 211-221 (1982) · Zbl 0487.60056 · doi:10.1007/BF00531745
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