A unified approach is proposed to describe the statistics of the short timedynamics of multiscale complex systems. The probability density function of therelevant time series (signal) is represented as a statistical superposition ofa large time-scale distribution weighted by the distribution of certaininternal variables that characterize the slowly changing background. Thedynamics of the background is formulated as a hierarchical stochastic modelwhose form is derived from simple physical constraints, which in turn restrictthe dynamics to only two possible classes. The probability distributions ofboth the signal and the background have simple representations in terms ofMeijer G-functions. The two universality classes for the background dynamicsmanifest themselves in the signal distribution as two types of tails: power lawand stretched exponential, respectively. A detailed analysis of empirical datafrom classical turbulence and financial markets shows excellent agreement withthe theory.
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