Skip to main content
SpringerLink
Log in

Some results on lag increments of principal value of brownian local time

  • Published:
Applied Mathematics-A Journal of Chinese Universities Aims and scope Submit manuscript

Abstract

Let W be a standard Brownian motion, and define Y(t)=∫ t0 ds/W(s) as Cauchy’s principal value related to the local time of W. We study some limit results on lag increments of Y(t) and obtain various results all of which are related to earlier work by Hanson and Russo in 1983.

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. Bertoin, J., Excursions of a BES0 (d) and its drift term (0<d<1), Probab. Theory Relat. Fields, 1990,84:231–250.

    Article  MATH  Google Scholar 

  2. Chen, B., Ph. D Dissertation, Carleton Univ., Ottawa, Canada, 1998.

    Google Scholar 

  3. Chen, G. J., Kong, F. C., Lin, Z. Y., Answers to some questions about increments of a Wiener process, Ann. Probab., 1986,14:1252–1261.

    MATH  Google Scholar 

  4. Csáki, E., Csörgő, M., Fóldes, A., et al., How big are the increments of the local time of a Wiener process? Ann. Probab., 1983,11(3):593–608.

    MATH  Google Scholar 

  5. Csáki, E., Csörgő, M., Fóldes, A., et al. Increment sizes of the principal value of Brownian local time, Probab. Theory Relat. Fields, 2000,117:515–531.

    Article  MATH  Google Scholar 

  6. Csörgő, M. Révész, P., Strong approximation in probability and statistic, Academic Press, New York, 1981.

    Google Scholar 

  7. Hu, Y., Shi, Z., An iterated logarithm law for Cauchy’s principal value of Brownian local times., In: M. Yor, ed., Exponential Functionals and Principal Values Related to Brownian Motion, Bibliotheca de la Revista Matemática Iberoamericana, Madrid, 1997,131–154.

    Google Scholar 

  8. Hanson, D. L., Russo, R. P., Some results on increments of the Wiener process with applications to lag sums of random variables, Ann. probab., 1983,11(3):609–623.

    MATH  Google Scholar 

  9. Itô, K., McKean, H. P., Diffusion Processes and Their Sample Paths. Springer, Berlin, 1965.

    MATH  Google Scholar 

  10. Yamada, T., Principal values of Brownian local times and their related topics. In: N. Ikeda et al., eds. Itô’s Stochastic Calculus and Probability Theory, Springer, Tokyo, 1996,413–422.

    Google Scholar 

  11. Yor, M., Exponential Functionals and Principal values Related to Brownian Motion, Bibliotheca de la Revista Matemática Iberoamericana, Madrid, 1997.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Math., Zhejiang Univ. (Xixi Campus), 310028, Hangzhou, China

    Wen Jiwei

Authors
  1. Wen Jiwei
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wen, J. Some results on lag increments of principal value of brownian local time. Appl. Math. Chin. Univ. 17, 199–207 (2002). https://doi.org/10.1007/s11766-002-0046-2

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11766-002-0046-2

MR Subject Classification

Keywords

Search

Navigation