Journal of Theoretical Probability

, Volume 20, Issue 2, pp 133–152 | Cite as

Continuity in Law with Respect to the Hurst Parameter of the Local Time of the Fractional Brownian Motion

  • Maria Jolis
  • Noèlia Viles

We give a result of stability in law of the local time of the fractional Brownian motion with respect to small perturbations of the Hurst parameter. Concretely, we prove that the law (in the space of continuous functions) of the local time of the fractional Brownian motion with Hurst parameter H converges weakly to that of the local time of \(B^{H_0}\), when H tends to H 0.


Convergence in law fractional Brownian motion local time 

2000 Mathematics Subject Classification

60B12 60J55 60G15 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Berman S.M. (1969). Local times and sample function properties of stationary Gaussian processes. Trans. Am. Math. Soc. 137, 277–299MATHCrossRefGoogle Scholar
  2. 2.
    Berman S.M. (1970). Gaussian processes with stationary increments: local times and sample function properties. Ann. Math. Stat. 41, 1260–1272Google Scholar
  3. 3.
    Berman, S. M. (1973). Local nondeterminism and local times of Gaussian processes. Indiana Univ. Math. J. 23, 69–94, 1973/74.Google Scholar
  4. 4.
    Billingsley P. (1968). Convergence of Probability Measures. Wiley, New YorkMATHGoogle Scholar
  5. 5.
    Yor, M. (1983). Le drap brownien comme limite en loi de temps locaux linéaires. In Seminar on Probability, XVII, Lecture Notes in Math., Vol. 986. Springer, Berlin, pp. 89–105.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterra, BarcelonaSpain

Personalised recommendations