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具有有限记忆的随机分形的重分形分解

Mutlifractal Decomposition of Random Fractal with Finite Memory
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摘要 Dryakhlov和Tempelman对具有有限记忆的随机分形集的Hausdorff维数进行了研究,本文对具有有限记忆的随机分形集K(ω)的重分形分解集Kα(ω)进行研究,得到了在一定条件下,这种随机分形集重分形分解集Kα(ω)的Hausdorff维数表达式. The Hausdorff dimension about random fractal sets with finite memory has been studied by Dryakhlov and Tempelman. In this paper, the multifractal decomposition of random fractal sets with finite memory is researched and under some certain conditions the Hausdorff dimension expression of the multifractal decomposition set Kα(ω) for random fractal set with finite memory is given.
作者 马强 戴朝寿
出处 《应用概率统计》 CSCD 北大核心 2010年第6期561-576,共16页 Chinese Journal of Applied Probability and Statistics
关键词 具有有限记忆的随机分形 重分形分解 Perron-Frobenius定理 局部维数 Random fractal with finite memory multifractal decomposition Perron-Frobenius theorem martingale local dimension.
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参考文献8

  • 1Dryakhlov, A.V. and Tempelman, A.A., On Hausdorff dimension of random fractals, New York J. Math., 7(2001), 99-115.
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  • 7TEMPELMAN, A.A., Dimension of random fractal in metric spaces, (Russian) Teor. Veroyatnost. i Primeen, 44(1999), 589-616; translation in Theory Probab. Appl., 44(2000), 537-557.
  • 8苏峰,赵兴球.随机递归结构的重分形分解[J].应用概率统计,1997,13(2):113-119. 被引量:1

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