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Stochastic analysis, groups of diffemorphisms and lagrangian description of viscous incompressible fluid

  • Yu. E. Gliklikh
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1520)

Keywords

Vector Field Riemannian Manifold Wiener Process Viscous Incompressible Fluid Lagrangian Description 
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References

  1. 1.
    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.Google Scholar
  2. 2.
    Belopol'skaya Ya.I. and Dalecky Yu.L. Stochastic equations and differential geometry. Kluwer, 1989.Google Scholar
  3. 3.
    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.Google Scholar
  4. 4.
    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.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Eliasson H.I. Geometry of manifolds of maps. J. Diff. Geometry, 1967, vol.1, N 2.Google Scholar
  6. 6.
    Elworthy K.D. Stochastic differential equations on manifolds. Cambridge University Press, 1982 (London Mathematical Society Lecture Notes Series, vol.70).Google Scholar
  7. 7.
    Gliklikh Yu.E. Analysis on Riemannian manifolds and problems of mathematical physics. Voronezh University Press, 1989. (in Russian)Google Scholar
  8. 8.
    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.Google Scholar
  9. 9.
    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.Google Scholar
  10. 10.
    Ito K. Extension of stochastic integrals. In: Proc. of Intern. Symp. SDE (Kyoto, 1976). New York, 1978.Google Scholar
  11. 11.
    Korolyuk V.S., Portenko N.I., Skorohod A.V. et al. Handbook in probability theory and mathematical statistics. Moscow, Nauka, 1985 (in Russian).Google Scholar
  12. 12.
    Liptser R.S. and Shiryayev A.N. Statistics of random processes. Springer, 1984.Google Scholar
  13. 13.
    Nelson E. Dynamical theories of Brownian motion. Princeton University Press, 1967.Google Scholar
  14. 14.
    Nelson E. Quantum fluctuations. Princeton University Press, 1985.Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Yu. E. Gliklikh
    • 1
  1. 1.Department of MathematicsVoronezh State UniversityVoronezhUSSR

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