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A Method For Inferring Hierarchical Dynamics In Stochastic Processes

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  • OLOF GÖRNERUP

    (Complex Systems Group, Department of Energy and Environment, Chalmers University of Technology, 412 96 Göteborg, Sweden)

  • MARTIN NILSSON JACOBI

    (Complex Systems Group, Department of Energy and Environment, Chalmers University of Technology, 412 96 Göteborg, Sweden)

Abstract

Complex systems may often be characterized by their hierarchical dynamics. In this paper we present a method and an operational algorithm that automatically infer this property in a broad range of systems — discrete stochastic processes. The main idea is to systematically explore the set of projections from the state space of a process to smaller state spaces, and to determine which of the projections impose Markovian dynamics on the coarser level. These projections, which we callMarkov projections, then constitute the hierarchical dynamics of the system. The algorithm operates on time series or other statistics, soa prioriknowledge of the intrinsic workings of a system is not required in order to determine its hierarchical dynamics. We illustrate the method by applying it to two simple processes — a finite state automaton and an iterated map.

Suggested Citation

  • Olof Görnerup & Martin Nilsson Jacobi, 2008. "A Method For Inferring Hierarchical Dynamics In Stochastic Processes," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-16.
    • Handle: RePEc:wsi:acsxxx:v:11:y:2008:i:01:n:s0219525908001507
    DOI: 10.1142/S0219525908001507
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