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References
Arnold V. Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluides parfaits. In: Ann. Inst. Fourier, 1966, t.16, N 1.
Belopol'skaya Ya.I. and Dalecky Yu.L. Stochastic equations and differential geometry. Kluwer, 1989.
De Witt-Morette C. and Elworthy K.D. A stepping stone to stochastic analysis. In: New stochastic methods in physics, Physics Reports, 1981, vol.77, N 3.
Ebin D.G., Marsden J. Groups of diffeomorphisms and the motion of an incompressible fluid. Annals of Math., 1970, vol.92, N 1, p.102–163.
Eliasson H.I. Geometry of manifolds of maps. J. Diff. Geometry, 1967, vol.1, N 2.
Elworthy K.D. Stochastic differential equations on manifolds. Cambridge University Press, 1982 (London Mathematical Society Lecture Notes Series, vol.70).
Gliklikh Yu.E. Analysis on Riemannian manifolds and problems of mathematical physics. Voronezh University Press, 1989. (in Russian)
Gliklikh Yu.E. Stochastic differential geometry of the groups of diffeomorphisms and the motion of viscous incompressible fluid. Fifth International Vilnius conference on probability theory and mathematical statistics, Abstracts of communications, 1989, vol.1, p.173–174.
Gliklikh Yu.E. Infinite-dimensional stochastic differential geometry in modern Lagrangian approach to hydrodynamics of viscous incompressible fluid. In: "Constantin Caratheodory: an International Tribute" (Th.M.Rassias, ed.), World Scientific, 1991.vol.1.
Ito K. Extension of stochastic integrals. In: Proc. of Intern. Symp. SDE (Kyoto, 1976). New York, 1978.
Korolyuk V.S., Portenko N.I., Skorohod A.V. et al. Handbook in probability theory and mathematical statistics. Moscow, Nauka, 1985 (in Russian).
Liptser R.S. and Shiryayev A.N. Statistics of random processes. Springer, 1984.
Nelson E. Dynamical theories of Brownian motion. Princeton University Press, 1967.
Nelson E. Quantum fluctuations. Princeton University Press, 1985.
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Gliklikh, Y.E. (1992). Stochastic analysis, groups of diffemorphisms and lagrangian description of viscous incompressible fluid. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A.M. (eds) Global Analysis - Studies and Applications V. Lecture Notes in Mathematics, vol 1520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084712
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DOI: https://doi.org/10.1007/BFb0084712
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