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Accuracy of coarse grained Markovian dynamics

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  • Hoffmann, Karl Heinz
  • Salamon, Peter

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.

Suggested Citation

  • Hoffmann, Karl Heinz & Salamon, Peter, 2011. "Accuracy of coarse grained Markovian dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(18), pages 3086-3094.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:18:p:3086-3094
    DOI: 10.1016/j.physa.2011.04.027
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    References listed on IDEAS

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    1. Young, H. Peyton, 2006. "Social Dynamics: TheorY AND Applications," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 22, pages 1081-1108, Elsevier.
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    Cited by:

    1. MacDonald, Iain L., 2020. "A coarse-grained Markov chain is a hidden Markov model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).

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