Skip to main content
SpringerLink
Log in

The Hölder continuity of Westwater process and its applications

  • Published:
Acta Mathematicae Applicatae Sinica Aims and scope Submit manuscript

Abstract

In this paper, the Hölder continuity of Westwater processX t is concerned. More precisely, we show that there exists a random variableτ C ∈ (0, ∞) for anyC ∈ (3, ∞) such that

$$|X_s - X_t | \leqslant C\sqrt {|s - t||\log |t - s||,} \forall |t - s|< \tau _c .$$

As its applications, we give two bounds respectively for the Hausdorff measure function of multiple time set of Westwater process, and the Hausdorff measure of the imageX(E) of a Borel setE by Westwater process.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R.J. Adler, The Geometry of Random Fields, Wiley Series in Prob. Math. Stati., 1981.

  2. D. Geman, J. Horowitz, J. Rosen, A Local Time Analysis of Intersections of Brownian Paths in the Plane,Ann. Prob.,12 (1984), 86–107.

    Google Scholar 

  3. R. Kaufman, Brownian motion and Dimension of Perfect Sets,Can. J. Math.,22 (1970), 674–680.

    Google Scholar 

  4. S. Kusuoka, The Path Property of Edward's Model for Long Polymer Chains in Three Dimensions, Res. Notes in Math., Pitman, London, 1985, 48–65.

    Google Scholar 

  5. M. Loève, Probability Theorey II, GTM 46, 4th ed., Springer-Verlag, 1977.

  6. E.A. Perkins, S.J. Taylor, Uniform Measure Results for the Image of Subsets under Brownian Motion,Prob. Th. Rel. Fields,76 (1987), 257–289.

    Article  Google Scholar 

  7. J Rosen, A Local Time Approach to the Self-intersections of Brownian Paths in Space,Comm. Math. Phys.,88 (1983), 327–338.

    Article  Google Scholar 

  8. J. Westwater, On Edward's Model for Long Polymer Chains,Comm. Math. Phys.,72 (1980), 131–174.

    Article  Google Scholar 

  9. X.Y. Zhou, The Hausdorff Dimension of the Double Points of Westwater Process (Preprint).

  10. X.Y. Zhou, The Local Time of Intersection of Westwater Process (Preprint).

Download references

Author information

Authors and Affiliations

  1. Beijing Normal University, Beijing

    Zhou Xianyin

Authors
  1. Zhou Xianyin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This project is supported in part by the National Natural Science Foundation of China.

In Commemoration of the 15th Anniversary of the Acta Mathematicae Applicatae Sinica.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, X. The Hölder continuity of Westwater process and its applications. Acta Mathematicae Applicatae Sinica 7, 289–297 (1991). https://doi.org/10.1007/BF02009681

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02009681

Keywords

Search

Navigation