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References
P.H. Baxendale, Wiener processes on manifolds of maps, Proc. Royal Soc. Edinburgh 87A (1980), 127–152.
P.H. Baxendale, Brownian motions in the diffeomorphism group I, Compositio Math. 53 (1984), 19–50.
P.H. Baxendale, Asymptotic behaviour of stochastic flows of diffeomorphisms: two case studies, preprint, Aberdeen University, 1984.
P.H. Baxendale, The Lyapunov spectrum of a stochastic flow of diffeomorphisms, Proceedings of a Workshop on Lyapunov exponents, ed. L. Arnold and V. Wihstutz, Springer Lecture Notes in Mathematics, 1985.
P.H. Baxendale and T.E. Harris, Isotropic stochastic flows, Ann. Probab. (to appear).
J-M. Bismut, Mécanique aléatoire, Springer Lecture Notes in Mathematics, 1981.
A.P. Carverhill, Flows of stochastic dynamical systems: ergodic theory, Stochastics 14 (1985), 273–318.
A.P. Carverhill, A formula for the Lyapunov numbers of a stochastic flow. Application to a perturbation theorem, Stochastics 14 (1985), 209–226.
A.P. Carverhill, Survey: Lyapunov exponents for stochastic flows on manifolds, Proceedings of a Workshop on Lyapunov exponents, ed. L. Arnold and V. Wihstutz, Springer Lecture Notes in Mathematics, 1985.
A.P. Carverhill, M.J. Chappell and K.D. Elworthy, Characteristic exponents for stochastic flows, Proceedings of BIBOS I: Stochastic Processes, Springer Lecture Notes in Mathematics, 1985.
M.J. Chappell, Bounds for average Lyapunov exponents of gradient stochastic systems, Proceedings of a Workshop on Lyapunov exponents, ed. L. Arnold and V. Wihstutz, Springer Lecture Notes in Mathematics, 1985.
K.D. Elworthy, Stochastic differential equations on manifolds, Cambridge University Press, 1982.
H. Furstenberg, Noncommuting random products, Trans. Amer. Math. Soc. 108 (1963), 377–428.
R.Z. Has'minskii, Necessary and sufficient conditions for the asymptotic stability of linear stochastic systems, Theory Prob. Appl. 12 (1967), 144–147.
N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, North Holland, Amsterdam, 1981.
N. Ikeda and S. Watanabe, Stochastic flows of diffeomorphisms, Advances in Probability 7 (Stochastic Analysis and Applications, ed. M. Pinsky) (1984), 179–198.
S. Kakutani, On equivalence of infinite product measures, Ann. of Math. 49 (1948), 214–224.
S. Kobayashi, Transformation groups in differential geometry, Springer-Verlag, Berlin, 1972.
H. Kunita, Stochastic differential equations and stochastic flow of diffeomorphisms, Ecole d'Été de Probabilités de Saint-Flour XII, Springer Lecture Notes in Mathematics, 1984, 143–303.
Y. Le Jan, Équilibre et exposants de Lyapunov de certain flots browniens, C.R. Acad. Sc. Paris Sér I 298 (1984), 361–364.
Y. Le Jan, Exposants de Lyapunov pour les mouvements browniens isotropes, C.R. Acad. Sc. Paris Sér I 299 (1984), 947–949.
Y. Le Jan, Equilibrium state for a turbulent flow of diffusion, Proceedings: Stochastic processes and infinite dimensional analysis, Bielefeld 1983, Pitman Research Notes in Mathematics 124, 1985.
Y. Le Jan and S. Watanabe, Stochastic flows of diffeomorphisms, Proceedings of Taniguchi symposium on stochastic analysis, Katata 1982, 307–332.
V.I. Oseledec, A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc. 19 (1968), 197–231.
D. Ruelle, Ergodic theory of differentiable dynamical systems, Inst. Hautes Etudes Sci. Publ. Math. 50 (1979), 275–305.
E.T. Whittaker and G.N. Watson, A course of modern analysis, Cambridge University Press, 1950.
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Baxendale, P.H. (1986). Asymptotic behaviour of stochastic flows of diffeomorphisms. In: Itô, K., Hida, T. (eds) Stochastic Processes and Their Applications. Lecture Notes in Mathematics, vol 1203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076869
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DOI: https://doi.org/10.1007/BFb0076869
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