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Open AccessArticle

Non-Linear Diffusion and Power Law Properties of Heterogeneous Systems: Application to Financial Time Series

1
Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
2
Instituto de Investigaciones Filosóficas, Bulnes 642, Buenos Aires 1176, Argentina
3
Facultad de Ingeniería y Tecnología, Universidad San Sebastián, Lota 2465, Santiago 7510157, Chile
Entropy 2018, 20(9), 649; https://doi.org/10.3390/e20090649
Received: 13 June 2018 / Revised: 11 August 2018 / Accepted: 12 August 2018 / Published: 30 August 2018
(This article belongs to the Special Issue Power Law Behaviour in Complex Systems)
In this work, we show that it is possible to obtain important ubiquitous physical characteristics when an aggregation of many systems is taken into account. We discuss the possibility of obtaining not only an anomalous diffusion process, but also a Non-Linear diffusion equation, that leads to a probability distribution, when using a set of non-Markovian processes. This probability distribution shows a power law behavior in the structure of its tails. It also reflects the anomalous transport characteristics of the ensemble of particles. This ubiquitous behavior, with a power law in the diffusive transport and the structure of the probability distribution, is related to a fast fluctuating phenomenon presented in the noise parameter. We discuss all the previous results using a financial time series example. View Full-Text
Keywords: power law; complex systems; non linear evolution equations power law; complex systems; non linear evolution equations
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MDPI and ACS Style

Fuentes, M.A. Non-Linear Diffusion and Power Law Properties of Heterogeneous Systems: Application to Financial Time Series. Entropy 2018, 20, 649. https://doi.org/10.3390/e20090649

AMA Style

Fuentes MA. Non-Linear Diffusion and Power Law Properties of Heterogeneous Systems: Application to Financial Time Series. Entropy. 2018; 20(9):649. https://doi.org/10.3390/e20090649

Chicago/Turabian Style

Fuentes, Miguel A. 2018. "Non-Linear Diffusion and Power Law Properties of Heterogeneous Systems: Application to Financial Time Series" Entropy 20, no. 9: 649. https://doi.org/10.3390/e20090649

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