Hierarchical Markovian modeling of multi-time scale systems

Abstract

We present a systematic way to analyze and model systems having many characteristic time-scales. The method we propose is employed for a test-case of a meandering jet model manifesting chaotic tracer dispersion with long time-correlations. We first choose a suitable state space partition and analyze the symbolic dynamics associated to the fluid particle position. In a second step we construct a stochastic process in terms of a multi-time Markovian model. This corresponds to a hierarchy of random travelers on a graph where each traveler moves at his own time scale. The results are compared on the basis of statistical measures such as entropies and correlation functions.