Berlin 2008 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 17: Poster I

DY 17.34: Poster

Dienstag, 26. Februar 2008, 16:00–18:00, Poster C

Dynamical characterization of Markov processes with varying order — •Michael Bauer and Günter Radons — Chemnitz University of Technology, 09107 Chemnitz, Germany

Our objective is to characterize the behavior of discrete-time Markov processes with randomly fluctuating order in a finite state space. Such processes may arise e.g. in the symbolic dynamics of dynamical systems with varying memory length. Changing the order leads to different transition matrices, resulting for the evaluation of block probabilities in random products of matrices with different ranks, which have to be applied to the initial state. We calculate numerically the Lyapunov exponents of the random matrix product and the Kolmogorov-Sinai entropy for a sequence of symbols generated by such a time-variant Markov chain. In special cases this can be done analytically. We also provide results for the distribution of the state probabilities of such a non-stationary process. A connection is made to special hidden Markov models thereby providing results also for the latter.