Abstract
We explore the exact packing dimension of certain random recursive constructions. In case of polynomial decay at 0 of the distribution function of random variable X, associated with the construction, we prove that it does not exist, and in case of exponential decay it is t α|log|logt||β, where α is the fractal dimension of the limit set and 1/β is the rate of exponential decay.
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Research supported by the Department of Mathematics and Statistics (Mathematics) at University of Jyväskylä.
Mathematics Subject Classification (2000):Primary 28A78, 28A80; Secondary 60D05, 60J80
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Berlinkov, A. Exact packing dimension in random recursive constructions. Probab. Theory Relat. Fields 126, 477–496 (2003). https://doi.org/10.1007/s00440-003-0281-3
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DOI: https://doi.org/10.1007/s00440-003-0281-3