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Linear stochastic dynamics with nonlinear fractal properties

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  • Sornette, Didier

Abstract

Stochastic processes with multiplicative noise have been studied independently in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with multiplicative noise produce intermittency of a special kind, characterized by a power law probability density distribution. We present a review of applications, highlight the common physical mechanism and summarize the main known results. The distribution and statistical properties of the duration of intermittent bursts are also characterized in detail.

Suggested Citation

  • Sornette, Didier, 1998. "Linear stochastic dynamics with nonlinear fractal properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 295-314.
    • Handle: RePEc:eee:phsmap:v:250:y:1998:i:1:p:295-314
    DOI: 10.1016/S0378-4371(97)00543-8
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    Citations

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    Cited by:

    1. Steven N. Durlauf, 2005. "Complexity and Empirical Economics," Economic Journal, Royal Economic Society, vol. 115(504), pages 225-243, June.
    2. Vandermarliere, B. & Ryckebusch, J. & Schoors, K. & Cauwels, P. & Sornette, D., 2017. "Discrete hierarchy of sizes and performances in the exchange-traded fund universe," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 111-123.
    3. Sornette, D., 2002. "“Slimming” of power-law tails by increasing market returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(3), pages 403-418.
    4. Mizuno, Takayuki & Takayasu, Misako & Takayasu, Hideki, 2004. "The mean-field approximation model of company's income growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 403-411.
    5. Silva, L.B.M. & Vermelho, M.V.D. & Lyra, M.L. & Viswanathan, G.M., 2009. "Multifractal detrended fluctuation analysis of analog random multiplicative processes," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2806-2811.
    6. Melecký, Jan & Sergyeyev, Artur, 2008. "A simple finite-difference stock market model involving intrinsic value," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 769-777.
    7. D. Sornette, 2000. ""Slimming" of power law tails by increasing market returns," Papers cond-mat/0010112, arXiv.org, revised Sep 2001.
    8. Jess Benhabib & Shenghao Zhu, 2008. "Age, Luck, and Inheritance," NBER Working Papers 14128, National Bureau of Economic Research, Inc.
    9. Sornette, Didier, 2000. "Stock market speculation: Spontaneous symmetry breaking of economic valuation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 355-375.
    10. Y. Malevergne & V. F. Pisarenko & D. Sornette, 2003. "Empirical Distributions of Log-Returns: between the Stretched Exponential and the Power Law?," Papers physics/0305089, arXiv.org.
    11. D. Sornette, 2000. "Stock Market Speculation: Spontaneous Symmetry Breaking of Economic Valuation," Papers cond-mat/0004001, arXiv.org.

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