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On the properties of random multiplicative measures with the multipliers exponentially distributed

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  • Zhou, Wei-Xing
  • Yu, Zun-Hong

Abstract

Under the formalism of annealed averaging of the partition function, a type of random multifractal measures with the multipliers exponentially distributed is investigated in detail. Branching emerges in the curve of generalized dimensions, and negative values of generalized dimensions arise. Three equivalent methods of classification of the random multifractal measures are proposed, which is based on: (i) the properties of the curves of generalized dimensions, (ii) the solution properties of equation τ(q)=0, and (iii) the relative position of the curve f(α) and the diagonal f(α)=α in the first quadrant. These classes of measures correspond to μ([0,1])=∞, μ([0,1])=1 and μ([0,1])=0, respectively. Phase diagram is introduced to illustrate the diverse performance of the random measures that is multiplicatively generated.

Suggested Citation

  • Zhou, Wei-Xing & Yu, Zun-Hong, 2001. "On the properties of random multiplicative measures with the multipliers exponentially distributed," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 294(3), pages 273-282.
    • Handle: RePEc:eee:phsmap:v:294:y:2001:i:3:p:273-282
    DOI: 10.1016/S0378-4371(01)00115-7
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    Citations

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    Cited by:

    1. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2007. "Scale invariant distribution and multifractality of volatility multipliers in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 343-350.
    2. Zhou, Weijie & Dang, Yaoguo & Gu, Rongbao, 2013. "Efficiency and multifractality analysis of CSI 300 based on multifractal detrending moving average algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1429-1438.
    3. Wang, Yudong & Wu, Chongfeng & Pan, Zhiyuan, 2011. "Multifractal detrending moving average analysis on the US Dollar exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3512-3523.
    4. Wang, Yudong & Wei, Yu & Wu, Chongfeng, 2011. "Detrended fluctuation analysis on spot and futures markets of West Texas Intermediate crude oil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(5), pages 864-875.
    5. Zhou, Wei-Xing & Sornette, Didier, 2009. "Numerical investigations of discrete scale invariance in fractals and multifractal measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(13), pages 2623-2639.

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