Skip to main content

An Extension of Local Time

In this paper, we construct an analog of local time for an arbitrary Lévy process with finite second moment. When our process is a Wiener process, this object coincides with the local time.

This is a preview of subscription content, access via your institution.


  1. 1.

    I. M. Gelfand and G. E. Shilov, Generalized Functions and Operations on Them [in Russian], Moscow (1958).

  2. 2.

    A. N. Borodin and I. A. Ibragimov, “Limit theorems for functionals of random walks,” Trudy Mat. Inst. AN SSSR, 195, 3—286 (1995).

    MATH  Google Scholar 

  3. 3.

    R. K. Getoor, “Another limit theorem for local time,” Z. Wahrscheinlichkeitstheorie verw. Gebiete, 34, 1–10 (1976).

    MathSciNet  Article  Google Scholar 

  4. 4.

    I. I. Gikhman and A. V. Skorohod, Introduction to the Theory of Random Processes [in Russian], Moscow (1977).

Download references

Author information



Corresponding authors

Correspondence to I. A. Ibragimov, N. V. Smorodina or M. M. Faddeev.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 486, 2019, pp. 148–163.

Translated by S. Yu. Pilyugin.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ibragimov, I.A., Smorodina, N.V. & Faddeev, M.M. An Extension of Local Time. J Math Sci 258, 838–844 (2021).

Download citation