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.
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Kasahara, Y., Ogawa, N. A Note on the Local Time of Fractional Brownian Motion. Journal of Theoretical Probability 12, 207–216 (1999). https://doi.org/10.1023/A:1021756929498
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DOI: https://doi.org/10.1023/A:1021756929498