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A Note on the Local Time of Fractional Brownian Motion

Author

Listed:
  • Yuji Kasahara

    (Ochanomizu University)

  • Namiko Ogawa

    (Juji Research Institute Corporation)

Abstract

Asymptotic behavior of the local time at the origin of q-dimensional fractional Brownian motion is considered when the index γ approaches the critical value 1/q. It is proved that, under a suitable (temporally inhomogeneous) normalization, it converges in law to the inverse of an extremal process which appears in the extreme value theory.

Suggested Citation

  • Yuji Kasahara & Namiko Ogawa, 1999. "A Note on the Local Time of Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 12(1), pages 207-216, January.
    • Handle: RePEc:spr:jotpro:v:12:y:1999:i:1:d:10.1023_a:1021756929498
    DOI: 10.1023/A:1021756929498
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    References listed on IDEAS

    as
    1. Kasahara, Y. & Kosugi, N., 1997. "A limit theorem for occupation times of fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 67(2), pages 161-175, May.
    2. Csörgo, Miklós & Lin, Zheng-Yan & Shao, Qi-Man, 1995. "On moduli of continuity for local times of Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 58(1), pages 1-21, July.
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