Skip to main content
SpringerLink
Log in

Asymptotic behaviour of stochastic flows of diffeomorphisms

  • Conference paper
  • First Online:
Book cover Stochastic Processes and Their Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1203))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P.H. Baxendale, Wiener processes on manifolds of maps, Proc. Royal Soc. Edinburgh 87A (1980), 127–152.

    Article  MathSciNet  MATH  Google Scholar 

  2. P.H. Baxendale, Brownian motions in the diffeomorphism group I, Compositio Math. 53 (1984), 19–50.

    MathSciNet  MATH  Google Scholar 

  3. P.H. Baxendale, Asymptotic behaviour of stochastic flows of diffeomorphisms: two case studies, preprint, Aberdeen University, 1984.

    Google Scholar 

  4. 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.

    Google Scholar 

  5. P.H. Baxendale and T.E. Harris, Isotropic stochastic flows, Ann. Probab. (to appear).

    Google Scholar 

  6. J-M. Bismut, Mécanique aléatoire, Springer Lecture Notes in Mathematics, 1981.

    Google Scholar 

  7. A.P. Carverhill, Flows of stochastic dynamical systems: ergodic theory, Stochastics 14 (1985), 273–318.

    Article  MathSciNet  MATH  Google Scholar 

  8. A.P. Carverhill, A formula for the Lyapunov numbers of a stochastic flow. Application to a perturbation theorem, Stochastics 14 (1985), 209–226.

    Article  MathSciNet  MATH  Google Scholar 

  9. 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.

    Google Scholar 

  10. 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.

    Google Scholar 

  11. 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.

    Google Scholar 

  12. K.D. Elworthy, Stochastic differential equations on manifolds, Cambridge University Press, 1982.

    Google Scholar 

  13. H. Furstenberg, Noncommuting random products, Trans. Amer. Math. Soc. 108 (1963), 377–428.

    Article  MathSciNet  MATH  Google Scholar 

  14. R.Z. Has'minskii, Necessary and sufficient conditions for the asymptotic stability of linear stochastic systems, Theory Prob. Appl. 12 (1967), 144–147.

    Article  MathSciNet  Google Scholar 

  15. N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, North Holland, Amsterdam, 1981.

    MATH  Google Scholar 

  16. N. Ikeda and S. Watanabe, Stochastic flows of diffeomorphisms, Advances in Probability 7 (Stochastic Analysis and Applications, ed. M. Pinsky) (1984), 179–198.

    Google Scholar 

  17. S. Kakutani, On equivalence of infinite product measures, Ann. of Math. 49 (1948), 214–224.

    Article  MathSciNet  MATH  Google Scholar 

  18. S. Kobayashi, Transformation groups in differential geometry, Springer-Verlag, Berlin, 1972.

    Book  MATH  Google Scholar 

  19. 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.

    Google Scholar 

  20. Y. Le Jan, Équilibre et exposants de Lyapunov de certain flots browniens, C.R. Acad. Sc. Paris Sér I 298 (1984), 361–364.

    MATH  Google Scholar 

  21. Y. Le Jan, Exposants de Lyapunov pour les mouvements browniens isotropes, C.R. Acad. Sc. Paris Sér I 299 (1984), 947–949.

    MathSciNet  MATH  Google Scholar 

  22. 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.

    Google Scholar 

  23. Y. Le Jan and S. Watanabe, Stochastic flows of diffeomorphisms, Proceedings of Taniguchi symposium on stochastic analysis, Katata 1982, 307–332.

    Google Scholar 

  24. V.I. Oseledec, A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc. 19 (1968), 197–231.

    MathSciNet  Google Scholar 

  25. D. Ruelle, Ergodic theory of differentiable dynamical systems, Inst. Hautes Etudes Sci. Publ. Math. 50 (1979), 275–305.

    Article  MathSciNet  MATH  Google Scholar 

  26. E.T. Whittaker and G.N. Watson, A course of modern analysis, Cambridge University Press, 1950.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Aberdeen, AB9 2TY, Aberdeen, Scotland

    Peter H. Baxendale

Authors
  1. Peter H. Baxendale
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Kiyosi Itô Takeyuki Hida

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

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

Download citation

  • DOI: https://doi.org/10.1007/BFb0076869

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16773-0

  • Online ISBN: 978-3-540-39852-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation