Accuracy of coarse grained Markovian dynamics

Karl Heinz Hoffmann and Peter Salamon

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 18, 3086-3094

Abstract: Markov chain models on a mesoscopic level are a widely used description for complex systems. They are based on the assumption that certain sets of microstates can be coarse grained as their internal dynamics is faster than the time scales considered in the modeling. Here we analyze quantitatively the errors made by using lumping techniques and present the first rigorous proof for bounds on such errors. Our bounds express the deviations from a full microscopic description for all subsequent time steps in terms of the deviations in the first time step.

Keywords: Irreversible thermodynamics; Markov processes; Markov chain; Lumping techniques; Coarse grained Markovian dynamics (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:18:p:3086-3094

DOI: 10.1016/j.physa.2011.04.027

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