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Statistical mixing and aggregation in Feller diffusion

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  • Celia Anteneodo
  • Silvio M. Duarte Queiros
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    Abstract

    We consider Feller mean-reverting square-root diffusion, which has been applied to model a wide variety of processes with linearly state-dependent diffusion, such as stochastic volatility and interest rates in finance, and neuronal and populations dynamics in natural sciences. We focus on the statistical mixing (or superstatistical) process in which the parameter related to the mean value can fluctuate - a plausible mechanism for the emergence of heavy-tailed distributions. We obtain analytical results for the associated probability density function (both stationary and time dependent), its correlation structure and aggregation properties. Our results are applied to explain the statistics of stock traded volume at different aggregation scales.

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    File URL: http://arxiv.org/pdf/0910.1394
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0910.1394.

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    Date of creation: Oct 2009
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    Publication status: Published in J. Stat. Mech. (2009) P10023
    Handle: RePEc:arx:papers:0910.1394

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    Web page: http://arxiv.org/

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    1. Kaizoji, Taisei & Sornette, Didier, 2008. "Market Bubbles and Chrashes," MPRA Paper 15204, University Library of Munich, Germany.
    2. Sarah-Kathryn McDonald, 1987. "Book review," Policy Sciences, Springer, Springer, vol. 20(1), pages 77-79, April.
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