Dresden 2009 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 27: Poster II

DY 27.5: Poster

Donnerstag, 26. März 2009, 16:00–18:00, P1B

Entropy calculation of Markov processes with varying order via Blackwell’s measure — •Michael Bauer and Günter Radons — Chemnitz University of Technology, 09107 Chemnitz, Germany

Our objective is to calculate the entropy of discrete-time Markov processes with fluctuating order in a finite state space. Such processes may arise e.g. in the symbolic dynamics of dynamical systems with varying memory length. Due to the change of order, transition matrices with different ranks are applied to the initial state resulting in a random matrix product. For a sequence of symbols produced by such a time-variant Markov chain the Kolmogorov-Sinai entropy is calculated using Blackwell’s measure [1]. Therefore, special cases of this non-stationary process such as purely random variation and periodic variation are investigated and can be calculated analytically. A comparison to previous results [2] is drawn. We also provide results for processes with Markovian variation of memory establishing a fractal distribution in Blackwell’s measure.

[1]  D. Blackwell, The entropy of functions of finite-state Markov chains, Transactions of the First Prague Conference on Information Theory, Statistical Decision Functions, and Random Processes, pages 13–20, 1957.

[2]  M. Bauer, Dynamical characterization of Markov processes with varying order, Master Thesis, Chemnitz University of Technology, 2008.