Skip to main content

A simple proof of the support theorem for diffusion processes

  • Conference paper
  • First Online:
Séminaire de Probabilités XXVIII

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1583))

Partially supported by a grant of the DGICYT no PB 90-0452. This work was partially done while the author was visiting the “Laboratoire de Probabilités” at Paris VI.

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

Access this chapter

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. S. Aida, S. Kusuoka and D. Stroock, On the Support of Wiener Functionals, Asymptotic problems in probability Theory: Wiener functionals and asymptotics, Longman Sci. & Tech., Pitman Research Notes in Math. Series 294, N.Y., 3–34, (1993).

    Google Scholar 

  2. G. Ben Arous and M. Gradinaru, Normes Höldériennes et support des diffusions, C.R. Acad. Sc. Paris, t. 316, Série 1 n. 3, 283–286, (1993).

    MATH  Google Scholar 

  3. G. Ben Arous, M. Gradinaru and M. Ledoux, Hölder norms and the support theorem for diffusions, preprint.

    Google Scholar 

  4. Z. Ciesielski, On the isomorphisms of the spaces Hα and m, Bull. Acad. Pol. Sc., 8, 217–222 (1960).

    MATH  Google Scholar 

  5. I. Gyöngy and T. Pröhle, On the approximation of stochastic differential equations and on Stroock-Varadhan's support theorem, Computers Math. Applic, 19, 65–70 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  6. N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, Amsterdam, Oxford, New York: North Holland: Tokyo: Kodansha 1981.

    MATH  Google Scholar 

  7. V. Mackevičius, On the Support of the Solution of Stochastic Differential Equations, Lietuvos Matematikow Rinkings XXXVI (1), 91–98 (1986).

    Google Scholar 

  8. A. Millet and M. Sanz-Solé, The Support of an Hyperbolic Stochastic Partial Differential Equation, Probability Theory and Related Fields, to appear, Prépublication du Laboratoire de Probabilités de l'Université Paris VI n.° 150, 1993.

    Google Scholar 

  9. D. W. Stroock and S. R. S. Varadhan, On the Support of Diffusion Processes with Applications to the Strong Maximum Principle, Proc. Sixth Berkeley Symp. Math. Statist. Prob. III, 333–359, Univ. California Press, Berkeley, 1972.

    MATH  Google Scholar 

  10. D. W. Stroock and S. R. S. Varadhan, On Degenerate Elliptic-Parabolic Operators of Second Order and their Associated Diffusions, Comm. on Pure and Appl. Math. Vol. XXV, 651–713 (1972).

    Article  MathSciNet  MATH  Google Scholar 

  11. D. W. Stroock and S. R. S. Varadhan, Multidimensional processes, Springer-Verlag, Berlin Heildelberg, New York, 1979. *** DIRECT SUPPORT *** A00I6B40 00002

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jacques Azéma Marc Yor Paul André Meyer

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag

About this paper

Cite this paper

Millet, A., Sanz-Solé, M. (1994). A simple proof of the support theorem for diffusion processes. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXVIII. Lecture Notes in Mathematics, vol 1583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073832

Download citation

  • DOI: https://doi.org/10.1007/BFb0073832

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58331-8

  • Online ISBN: 978-3-540-48656-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics