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On stochastic horizontal lifts. (English) Zbl 0487.60056

MSC:
60H99 Stochastic analysis
58J65 Diffusion processes and stochastic analysis on manifolds
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[1] Dynkin, E.B.: Diffusion of tensors. Soviet Math. Dokl. 9, 532-535 (1968) · Zbl 0188.27002
[2] Ikeda, N., Manabe, S.: Integral of differential forms along the path of diffusion processes. Publ. R.I.M.S. Kyoto Univ. 15, 827-852 (1979) · Zbl 0462.60056 · doi:10.2977/prims/1195187879
[3] Ikeda, N., Watanabe, S.: Stochastic differential equations and diffusion processes. Tokyo: Kodansha 1981 · Zbl 0495.60005
[4] It?, K.: The Brownian motion and tensor fields on Riemannian manifold. Proc. Intern. Cong. of Math. Stockholm, 536-539 (1962)
[5] It?, K.: Stochastic differentials. Appl. Math. Optim. 1, 347-381 (1975)
[6] It?, K.: Stochastic parallel displacement. Lecture Notes in Math., 451, pp. 1-7. Berlin-Heidelberg-New York: Springer 1957
[7] It?, K.: Brownian motion on Riemannian manifold and harmonic tensor fields (in Japanese). S?gaku 28, 137-146 (1976)
[8] Kobayashi, S., Nomizu, K.: Foundations of differential geometry. New York: Interscience, vol. 1 (1963), vol. 2 (1968) · Zbl 0119.37502
[9] Kunita, H.: On the decomposition of solutions of stochastic differential equations. Lecture Notes in Math., vol. 851, pp. 213-255. Berlin-Heidelberg-New York: Springer 1981 · Zbl 0474.60046
[10] Kunita, H.: Some extensions of It?’s formula. Seminaire de Probabilites XV. Lecture Notes in Math., vol. 850. Berlin-Heidelberg-New York: Springer 1980
[11] Malliavin, P.: Formules de la moyenne, calcul de perturbation et th?or?mes d’annulation pour les formes harmoniques. J. Func. Anal. 17, 247-291 (1974) · Zbl 0425.58022 · doi:10.1016/0022-1236(74)90041-X
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