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References
P. Baxendale, Wiener processes on manifolds of maps, Proc. Royal Soc. Edinburgh, 87A (1980), 127–152.
J. M. Bismut, A generalized formula of Itô and some other properties of stochastic flows, Z. W. 55 (1981), 331–350.
J. M. Bismut, Mécanique aléatoire, Lecture Notes in Math. 866 (1981).
Yu. N. Blagovescenskii-M. I. Freidlin, Certain properties of diffusion processes depending on a parameter, Soviet Math. Dokl. 2 (1961), 633–636.
K. T. Chen, Decomposition of differential equations, Math. Annalen 146 (1962), 263–278.
J. L. Doob, Stochastic processes, John Wiley and Sons, New York, 1953.
K. D. Elworthy, Stochastic dynamical system and their flows, Stochastic analysis ed. by A. Friedman and M. Pinsky, 79–95, Academic Press, New York, 1978.
M. Emery, Une topologie sur l'espace des semimartingales, Séminaire de Prob. XIII, Lecture Notes in Math. 721 (1979), 260–280.
M. Fliess-D. Normand-Cyrot, Algébres de Lie nilpotents, formule de Baker-Campbell-Hausdorff et intégrales iterées de K. T. Chen, Séminaire de Prob. XVI, Lecture Notes in Math., to appear.
T. Funaki, Construction of a solution of random transport equation with boundary condition, J. Math. Soc. Japan 31 (1979), 719–744.
N. Ikeda-S. Manabe, Stochastic integral of differential forms and its applications, Stochastic Analysis ed. by A. Friedman and M. Pinsky, 175–185, New York, 1978.
N. Ikeda-S. Manabe, Integral of differential forms along the path of diffusion processes, Publ. RIMS, Kyoto Univ. 15 (1979), 827–852.
N. Ikeda-S. Watanabe, Stochastic differential equations and diffusion processes, North Holland-Kodansha, 1981.
N. Ikeda-S. Watanabe, Stochastic flow of diffeomorphisms, to appear.
K. Itô, Stochastic differential equations in a differentiable manifold Nagoya Math. J. 1 (1950), 35–37
Mem. Coll. Sci. Univ. Kyoto Math. 28 (1953), 81–85.
K. Itô, Lectures on stochastic processes, Tata Institute of Fundamental Research, Bombay, 1960.
K. Itô, The Brownian motion and tensor fields on Riemannian manifold, Proc. Intern. Congr. Math. Stockholm, 536–539, 1963.
K. Itô, Stochastic parallel displacement, Probabilistic methods in differential equations, Lecture Notes in Math. 451 (1975), 1–7.
S. Kobayashi-K. Nomizu, Fundations of differential geometry I, John Wiley and Sons, New York, 1963.
A. J. Krener-C. Lobry, The complexity of solutions of stochastic differential equations, Stochastics 4 (1981), 193–203.
N. V. Krylov-B. L. Rozovsky, On the first integrals and Liouville equations for diffusion processes, Proc. Third Conf. Stoch. Diff. System, Lecture Notes in Control and Information Science, to appear.
H. Kunita, On the representation of solutions of stochastic differential equations, Séminaire des Probabilités XIV, Lecture Notes in Math. 784 (1980), 282–303.
H. Kunita, On the decomposition of solutions of stochastic differential equations, Proc. Durham Conf. Stoch. Integrals, Lecture Notes in Math. 851 (1981), 213–255.
H. Kunita, Some extensions of Itô's formula, Séminaire de Probabilités, XV, Lecture Notes in Math. 850 (1981), 118–141.
H. Kunita, On backward stochastic differential equations, Stochastics 6 (1982), 293–313.
H. Kunita, Stochastic differential equations and stochastic flows of homeomorphisms, to appear.
H. Kunita, Stochastic partial differential equations connected with non-linear filtering, to appear in the Proceedings of C.I.M.E. Session on Stochastic control and filtering, Cortona, 1981.
H. Kunita-S. Watanabe, On square integrable martingales, Nagoya Math. J. 30 (1967), 209–245.
P. Malliavin, Un principe de transfert et son application au calcul de variations, C. R. Acad. Sci. Paris, 284, Serie A (1977), 187–189.
P. Malliavin, Stochastic calculus of variation and hypoelliptic operators, Proc. Intern Symp. SDE Kyoto 1976 (ed. by K. Itô) 195–263, Kinokuniya, Tokyo.
P. Malliavin, Géométrie differentielle stochastique, Les Presses de l'Université de Montréal, Montréal, 1978.
Y. Matsushima, Differentiable manifolds, Marcel Dekker, New York, 1972.
P. A. Meyer, Probability and potentials, Blaisdel, Waltham, Massachusetts, 1966.
P. A. Meyer, Integrales stochastiques I-IV, Séminaire de Prob. I, Lecture Notes in Math. 39 (1967), 72–162.
P. A. Meyer, Geometrie stochastique sans larmes, Séminaire de Prob. XV, Lecture Notes in Math. 850 (1981), 44–102.
P. A. Meyer, Flot d'une equation differentielle stochastique, Séminaire de Prob. XV, Lecture Notes in Math. 850 (1981), 103–117.
J. Neveu, Bases mathématiques du calcul des probabilités, Masson et Cie., Paris, 1964.
B. L. Rozovsky, On the Itô-Ventzel formula, Vestnik of Moscow University, N. 1 (1973), 26–32. (In Russian).
I. Shigekawa, On stochastic horizontal lifts, Z. W. 59 (1982), 211–222.
D. W. Stroock-S. R. S. Varadhan, On the support of diffusion processes with application to the strong maximum principle, Proc. Sixth Berkeley Symp. Math. Statist. Prob. III, 333–359, Univ. California Press, Berkeley, 1972.
D. W. Stroock-S. R. S. Varadhan, Multidimensional diffusion processes, Springer-Verlag, Berlin, 1979.
A. D. Ventcel', On equations of the theory of conditional Markov processes, Theory of Prob. Appl. 10 (1965), 357–361.
S. Watanabe, Flow of diffeomorphisms difined by stochastic differential equation on manifolds and their differentials and variations (in Japanese), Suriken Kokyuroku 391 (1980), 1–23.
T. Yamada-Y. Ogura, On the strong comparison theorems for solutions of stochastic differetial equations, Z. W. 56 (1981), 3–19.
Y. Yamato, Stochastic differential equations and nilpotent Lie algebra, Z. W. 47 (1979), 213–229.
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Kunita, H. (1984). Stochastic differential equations and stochastic flows of diffeomorphisms. In: Hennequin, P.L. (eds) École d'Été de Probabilités de Saint-Flour XII - 1982. Lecture Notes in Mathematics, vol 1097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099433
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DOI: https://doi.org/10.1007/BFb0099433
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