Skip to main content
SpringerLink
Log in

On the weak convergence to Brownian local time

  • Conference paper
  • First Online:
Probability Theory and Mathematical Statistics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1299))

  • 929 Accesses

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
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. Skorokhod, A. V. Studies in the theory of random processes. Kiev: Kiev University Press 1961.

    MATH  Google Scholar 

  2. Skorokhod, A. V., Slobodenyuk, N. P. Limit theorems for random walks. Kiev: Naukova Dumka 1970.

    MATH  Google Scholar 

  3. Borodin, A. N. An asymptotic behaviour of local times of a recurrent random walk with finite variance. Theory Probab. Appl. vol.26, 769–783 (1981).

    MATH  Google Scholar 

  4. Sytaya, G. N. Limit theorems for some functionals of random walks. Theory Probab. Appl. vol.12, 483–492 (1967).

    Article  MathSciNet  Google Scholar 

  5. Borodin, A. N. A limit theorem for sums of independent random variables defined on a recurrent random walk. Dokl. USSR Academy of Sciences vol.246, N4, 786–788 (1979).

    MathSciNet  MATH  Google Scholar 

  6. Borodin, A. N. Limit theorems for sums of independent random variables defined on a nonrecurrent random walk. Zapiski Nauchnych Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR vol.85, 17–29 (1979).

    Google Scholar 

  7. Borodin, A. N. Limit theorems for sums of independent random variables defined on a recurrent random walk. Theory Probab. Appl. vol.28, 98–114 (1983).

    MathSciNet  MATH  Google Scholar 

  8. Kesten, H., Spitzer, F. A limit theorem related to a new class of self similar processes. Z. Wahrscheinlichkeitstheor. verw. Geb. B.50, 5–25 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  9. Borodin, A. N. On the character of convergence to Brownian local time. II. Probab. Th. Rel. Fields vol.72, 251–277 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  10. Révész, P. Local time and invariance. Lecture Notes in Math. vol.861, 128–145 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  11. Révész, P. A strong invariance principle of the local time of R.V.'s with continuous distribution. Carleton Math. Lect. Note vol.37, (1982).

    Google Scholar 

  12. Csaki, E., Révész, P. Strong invariance for local times. Z. Wahrscheinlichkeitstheor. verw. Geb. B.62, 263–278 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  13. Davydov, Yu. A. Sur une classe des fonctionnelles des processus stables et des marches aléatoires. Ann. Inst. Henri Poincaré, sect.B vol.X, 1–29 (1974).

    MATH  Google Scholar 

  14. Perkins, E. Weak invariance principles for local time. Z. Wahrscheinlichkeitstheor. verw. Geb. B.60, 437–451 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  15. Petrova, M. V. On weak convergence of functionals of random walks. Dokl. USSR Academy of Sciences vol.278, 806–809 (1984).

    MathSciNet  MATH  Google Scholar 

  16. Borodin, A. N. An asymptotic behaviour of local times of a recurrent random walk with infinite variance. Theory Probab. Appl. vol.29, 312–326 (1984).

    MATH  Google Scholar 

  17. Czörgo, M., Révész, P. On strong invariance for local time of partial sums. Stochastic Proc. Appl. vol.20, 59–84 (1985).

    Article  MathSciNet  Google Scholar 

  18. Ibragimov I. A. Théorèmes limites pour les marches aléatoires. Lecture Notes in Math. vol.117, 199–297 (1985).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Leningrad Branch Steklov Institute of Mathematics Academy of Sciences of the USSR, Fontanka 27, 191011, Leningrad, USSR

    A. N. Borodin

Authors
  1. A. N. Borodin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Shinzo Watanabe Jurii Vasilievich Prokhorov

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Borodin, A.N. (1988). On the weak convergence to Brownian local time. In: Watanabe, S., Prokhorov, J.V. (eds) Probability Theory and Mathematical Statistics. Lecture Notes in Mathematics, vol 1299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078460

Download citation

  • DOI: https://doi.org/10.1007/BFb0078460

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18814-8

  • Online ISBN: 978-3-540-48187-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation