منابع مشابه
Billingsley ’ S Packing Dimension
For a stochastic process on a finite state space, we define the notion of a packing measure based on the naturally defined cylinder sets. For any two measures ν, γ, corresponding to the same stochastic process, if F ⊆ { ω ∈ Ω : lim n log γ(cn(ω)) log ν(cn(ω)) = θ } , then we prove that Dimν(F ) = θ Dimγ(F ).
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We show that the dimension adim introduced by R. Kaufman (1987) coincides with the packing dimension Dim, but the dimension aDim introduced by Hu and Taylor (1994) is different from the Hausdorff dimension. These results answer questions raised by Hu and Taylor. AMS Classification numbers: Primary 28A78, 28A80.
متن کاملPacking Dimension Profiles and Lévy Processes
We extend the concept of packing dimension profiles, due to Falconer and Howroyd (1997) and Howroyd (2001), and use our extension in order to determine the packing dimension of an arbitrary image of a general Lévy process.
متن کاملPacking-dimension Profiles and Fractional Brownian Motion
In order to compute the packing dimension of orthogonal projections Falconer and Howroyd (1997) introduced a family of packing dimension profiles Dims that are parametrized by real numbers s > 0. Subsequently, Howroyd (2001) introduced alternate s-dimensional packing dimension profiles P-dims and proved, among many other things, that P-dimsE = DimsE for all integers s > 0 and all analytic sets ...
متن کاملIntrinsic Dimension Estimation Using Packing Numbers
We propose a new algorithm to estimate the intrinsic dimension of data sets. The method is based on geometric properties of the data and requires neither parametric assumptions on the data generating model nor input parameters to set. The method is compared to a similar, widelyused algorithm from the same family of geometric techniques. Experiments show that our method is more robust in terms o...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2008
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-07-09069-7