Long-range correlations have been evidenced in a number of experiments, generally using overlearned and overpracticed tasks. The authors hypothesized that long-range correlation could represent the byproduct of learning. They analyzed the series of periods produced by a group of expert and a group of novices during prolonged trials on a ski simulator. Results showed a very low variability in expert's series, as compared to novices. Fractal analyses showed that fluctuations were significantly more structured and correlated in experts. These results suggest that learning could be conceived as the progressive installation of complexity in the system.
Cascade Stochastic Differential Equation (SDE), a continuous time model for energy dissipation in turbulence, is a generalization of the Yaglom discrete cascade model. We extend this SDE to a model in random environment by assuming that its two parameters are switched by a continuous time Markov chain whose states represent the states of the environment. Moreover, a Dirichlet process is placed as a prior on the space of sample paths of this chain. We propose a Bayesian estimation method of this model which is tested both on simulated data and on real data of wind speed measured at the entrance of the mangrove ecosystem in Guadeloupe.
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