Skip to main content

A note on integrability of C r-norms of stochastic flows and applications

Part of the Lecture Notes in Mathematics book series (LNM,volume 1325)

Abstract

The integrability of uniform norms for higher derivatives of stochastic flows proved in this note implies existence of non-random stable manifolds, a Pesin type entropy formula and Hölder continuity of certain invariant subbundles for C 2-stochastic flows.

Keywords

  • Stochastic Differential Equation
  • Stable Manifold
  • Uniform Norm
  • Stochastic Flow
  • Finite Partition

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supported by Binational USA-Israel Science Foundation.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. Baxendale, Brownian motions in the diffeomorphism group I, Compositio Matematica 53(1984), 19–50.

    MathSciNet  MATH  Google Scholar 

  2. P. Baxendale, Lyapunov exponents and relative entropy for a stochastic flow of diffeomorphisms, Preprint.

    Google Scholar 

  3. M. Brin and Yu. Kifer, Dynamics of Markov chains and stable manifolds for random diffeomorphisms, Ergodic Theory of Dynamical Systems, to appear.

    Google Scholar 

  4. A.P. Carverhill, Flows of stochastic dynamical systems, Ergodic theory, Stochastics 14 (1985), 273–318.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. J. Franks, Manifolds of C r mappings and applications to differentiable dynamical systems, Studies in analysis, Advances in Mathematics Supplementary Series 4 (1979), 271–291.

    MathSciNet  Google Scholar 

  6. Yu. Kifer, Ergodic Theory of Random Transformations, Birkhäuser, Basel, 1986.

    CrossRef  MATH  Google Scholar 

  7. F. Ledrappier and L.S. Young, Entropy formula for random transformations, Preprint.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Kifer, Y. (1988). A note on integrability of C r-norms of stochastic flows and applications. In: Truman, A., Davies, I.M. (eds) Stochastic Mechanics and Stochastic Processes. Lecture Notes in Mathematics, vol 1325. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077921

Download citation

  • DOI: https://doi.org/10.1007/BFb0077921

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50015-5

  • Online ISBN: 978-3-540-45887-6

  • eBook Packages: Springer Book Archive