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Universal relation between skewness and kurtosis in complex dynamics

Matthieu Cristelli, Andrea Zaccaria, Luciano Pietronero

ABSTRACT

In this chapter we discuss the work presented in the paper—Cristelli et al., Phys. Rev. E, 85, 066108, 2012, where we identify an important correlation between skewness and kurtosis for a broad class of complex dynamics and present a specific analysis of earthquake and financial time series. We highlight that two regimes of non Gaussianity can be identified: a parabolic one, which is common in various fields of physics, and a power law one, with exponent 4/3, which, at the moment, appears to be specific of earthquakes and financial markets.

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