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Statistical propertis in the Poincaré reccurrence in stochastic processes


We consider the study of the statistical propertiesin the Theory of Poincaré Reccurrence over stochastic processes. We are interested in processes with slow loss of memory or long range memory. These type of models present different properties with respect to the models already studied in the literature where the loss of memory is faster, as for instance, the markovian models. Our interest is to dene and to analyze quantiers that describe characteristics of the process. For instance, Kolmogorov comprexity, Shannon entropy, Renyi entropies, state space and its potential wels, maximum and minimum energy states, among others. In particular our interest is to present techniques that would work with short samples, where the previous techniques didn't work. We expect also to consider the same topics in the context of random elds. (AU)