Skip to main content
Log in

Renormalization constant for the local times of self-intersections of a diffusion process in the plane

  • Published:
Ukrainian Mathematical Journal Aims and scope

We study the local times of self-intersection of a diffusion process in the plane. Our main result is connected with the investigation of the asymptotic behavior of the renormalization constant of this local time.

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

Access this article

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. L. Wolpert, “Local time and a particle for Euclidian field theory,” J. Func. Anal., 30, 341–357 (1978).

    Article  MATH  MathSciNet  Google Scholar 

  2. E. B. Dynkin, “Regularized self intersection local times of planar Brownian motion,” Ann. Probab., 16, No. 1, 58–74 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  3. J.-F. Le Gall, “Fluctuation results for the Wiener sausage,” Ann. Probab., 16, 991–1018 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  4. J. Rosen, “Dirichlet processes and an intrinsic characterization for renormalized intersection local times,” Ann. Inst. H. Poincaré, 37, 403–420 (2001).

    Article  MATH  Google Scholar 

  5. J. Rosen, “Continuity and singularity of the intersection local time of stable processes in \( \mathbb{R}^2 \),” Ann. Probab., 16, 75–79 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  6. J. Rosen, “Limit laws for the intersection local time of stable processes in \( \mathbb{R}^2 \),” Stochastics, 23, 219–240 (1988).

    MATH  MathSciNet  Google Scholar 

  7. R. F. Bass and D. Khoshnevisan, “Intersection local times and Tanaka formulas,” Ann. Inst. H. Poincaré Prob. Stat. , 29, 419–452 (1993).

    MATH  MathSciNet  Google Scholar 

  8. X. Chen, “Self-intersection local times of additive processes: large deviation and law of the iterated logarithm,” Stochast. Proc. Appl., 9, 1236–1253 (2006).

    Article  Google Scholar 

  9. R. Liptser and A. Shiryaev, Statistics of Random Processes, Springer, Berlin (2001).

    Google Scholar 

  10. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, New York (1964).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 11, pp. 1489–1498, November, 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Izyumtseva, O.L. Renormalization constant for the local times of self-intersections of a diffusion process in the plane. Ukr Math J 60, 1740–1751 (2008). https://doi.org/10.1007/s11253-009-0166-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-009-0166-4

Keywords

Navigation