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Bismut, J.M.: A generalized formula of Ito and some other properties of stochastic flows. Z. Wahrscheinlichkeitstheorie verw. Gebiete 55, 331–350 (1981)
Cameron, R.H., Martin, W.T.: Transformations of Wiener integrals under translations. Ann. Math. 45, 386–396 (1944)
Cameron, R.H., Martin, W.T.: Transformations of Wiener integrals under a general class of linear transformations. Trans. Amer. Math. Soc. 58, 184–219 (1945)
Cameron, R.H., Martin, W.T.: The transformation of Wiener integrals by nonlinear transformations. Trans. Amer. Math. Soc. 66, 253–283 (1949)
Ershov, M.P.: On the absolute continuity of measures corresponding to diffusion type processes. Theor. Probability Appl. 17, 169–174 (1972)
Hitsuda, M.: Representation of Gaussian processes equivalent to Wiener process. Osaka J. Math. 5, 299–312 (1968)
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)
Ikeda, N., Watanabe, S.: Stochastic differential equations and diffusion processes. Tokyo: Kodansha 1981
Itô, K.: Stochastic differentials. Appl. Math. Optim. 1, 347–381 (1975)
Kadota, T.T., Shepp, L.A.: Conditions for absolute continuity between a certain pair of probability measures. Z. Wahrscheinlichkeitstheorie verw. Gebiete 16, 250–260 (1970)
Kailath, T.: The structure of Radon-Nikodym derivatives with respect to Wiener and related measures. Ann. Math. Statist. 42, 1054–1067 (1971)
Kailath, T., Zakai, M.: Absolute continuity and Radon-Nikodym derivatives for certain measures relative to Wiener measure. Ann. Math. Statist. 42, 130–140 (1971)
Kobayashi, S., Nomizu, K.: Foundations of differential geometry, I, II, New York: Interscience 1963, 1969
Kunita, H.: On the decomposition of solutions of stochastic differential equations. Lecture Notes in Math. 851, pp. 213–255. Berlin-Heidelberg-New York: Springer 1981
Liptser, R.S., Shiryayev, A.N.: On absolute continuity of measures corresponding to diffusion type processes with respect to a Wiener measure. Izv. A.N. SSSR, ser. matem. 36, 847–889 (1972)
Liptser, R.S., Shiryayev, A.N.: Statistics of random processes, I, II, Berlin-Heidelberg-New York: Springer 1977
Malliavin, M.P., Malliavin, P.: Factorisation et lois limites de la diffusion horizontales au dessus d'un espace Riemannien symetrique. Lecture Notes in Math., 404, pp. 164–217. Berlin-Heidelberg-New York: Springer 1974
Malliavin, P.: Formules de la moyenne, calcul de perturbations et théorèmes d'annulation pour les formes harmoniques. J. Func. Anal. 17, 274–291 (1974)
McKean, H.P., Jr.: Brownian motions on the 3-dimensional rotation group. Mem. Coll. Sci. Univ. of Kyoto 33, 25–38 (1960)
McKean, H.P., Jr.: Stochastic integrals. New York-London: Academic Press 1969
Orey, S.: Conditions for the absolute continuity of two diffusions. Trans. Amer. Math. Soc. 193, 413–426 (1974)
Shepp, L.A.: Radon-Nikodym derivatives of Gaussian measures. Ann. Math. Statist. 37, 321–354 (1966)
Shigekawa, I.: On stochastic horizontal lifts. Z. Wahrscheinlichkeitstheorie verw. Gebiete 59, 211–221 (1982)
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This research was partially supported by Grant-in-Aid for Scientific Research, (No. 56740095), Ministry of Education
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Shigekawa, I. Transformations of the Brownian motion on a Riemannian symmetric space. Z. Wahrscheinlichkeitstheorie verw Gebiete 65, 493–522 (1984). https://doi.org/10.1007/BF00531836
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DOI: https://doi.org/10.1007/BF00531836