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

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## Abstract

**:**

## 1. Introduction

## 2. Microscopic Dynamics

## 3. Power Law Behavior in the Movement of Ensemble of Particles

## 4. A Marginalization of Weakly Coupled Systems

## 5. Application to the Financial Time Series

## 6. Final Remarks

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Second moment of the return.The red line corresponds to the empirical fit $\alpha =0.44$, while the black line shows $\alpha =1$.

**Figure 2.**Collapse of the empirical complementarycumulative distribution for time $t=100$, 200, 1000 and 2000. The continuous blue line is the theoretical curve, after the marginalization Equation (13). Inset: Complementary cumulative distribution for b, and the fit to a gamma distribution.

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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