Abstract
This communication presents and explores ultra diffusions—a class of random transport processes which generalizes the class of ‘classic’ diffusions. Examples of ultra diffusions include Lévy motions, fractional Brownian motions, fractional stable Lévy motions, Ornstein–Uhlenbeck motions driven by symmetric stable Lévy motions and M/G/∞ processes. A methodological framework of ultra diffusions is established—accommodating transport processes which display, simultaneously, both ‘anomalous-diffusion’ temporal behavior and ‘fat-tailed’ amplitudinal Lévy fluctuations. Ultra diffusions with power-law temporal and amplitudinal statistics are shown to emerge universally from a general superposition model of stochastic processes.
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