Abstract
In their classic paper, S. Orey and S.J. Taylor compute the Hausdorff dimension of the set of points at which the law of the iterated logarithm fails for Brownian motion. By introducing “fast sets”, we describe a converse to this problem for fractional Brownian motion. Our result is in the form of a limit theorem. From this, we can deduce refinements to the aforementioned dimension result of Orey and Taylor as well as the work of R. Kaufman. This is achieved via establishing relations between stochastic co-dimension of a set and its Hausdorff dimension along the lines suggested by a theorem of S.J. Taylor.
Research supported by a grant from the National Security Agency
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Khoshnevisan, D., Shi, Z. (2000). Fast sets and points for fractional Brownian motion. In: Azéma, J., Ledoux, M., Émery, M., Yor, M. (eds) Séminaire de Probabilités XXXIV. Lecture Notes in Mathematics, vol 1729. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103816
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DOI: https://doi.org/10.1007/BFb0103816
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