The McMillan Theorem for Colored Branching Processes and Dimensions of Random Fractals
For the simplest colored branching process, we prove an analog to the McMillan theorem and calculate the Hausdorff dimensions of random fractals defined in terms of the limit behavior of empirical measures generated by finite genetic lines. In this setting, the role of Shannon’s entropy is played by...
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| Format: | Article |
| Language: | English |
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MDPI AG
2014-12-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/16/12/6624 |
| Summary: | For the simplest colored branching process, we prove an analog to the McMillan theorem and calculate the Hausdorff dimensions of random fractals defined in terms of the limit behavior of empirical measures generated by finite genetic lines. In this setting, the role of Shannon’s entropy is played by the Kullback–Leibler divergence, and the Hausdorff dimensions are computed by means of the so-called Billingsley–Kullback entropy, defined in the paper. |
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| ISSN: | 1099-4300 |