Decomposing Complexity Mixture Processes on Metric Spaces

Complexity of a random process whose Small Ball Probability behaves asymptotically in a monomial way is a concept tied to the minimum number of random sources used to define the process. In this paper the new notion of complexity mixture process is defined and discussed from a theoretical point of view, and an algorithm based on a Bayesian principle is implemented to unravel the underlying complete complexity structure of the process starting from a sample of observed trajectories. To evaluate the performance of this approach under various controlled settings, a Monte Carlo simulation is performed. Finally, the method is applied to identify the mixture complexity structure of two real data sets.