Informational and Causal Architecture of
Continuous-Time Renewal Processes

Sarah Marzen

Physics of Living Systems Group
Department of Physics
Massachusetts Institute of Technology
Cambridge, MA 02139


James P. Crutchfield

Complexity Sciences Center
Physics Department
University of California at Davis
Davis, CA 95616

ABSTRACT: We introduce the minimal maximally predictive models (ε-machines) of processes generated by certain hidden semi-Markov models. Their causal states are either discrete, mixed, or continuous random variables and causal-state transitions are described by partial differential equations. As an application, we present a complete analysis of the ε-machines of continuous-time renewal processes. This leads to closed-form expressions for their entropy rate, statistical complexity, excess entropy, and differential information anatomy rates.

Sarah Marzen and James P. Crutchfield, "Informational and Causal Architecture of Continuous-time Renewal Processes", Journal of Statistical Physics 168:1 (2017) 109-127.
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Santa Fe Institute Working Paper 16-11-024. [cond-mat.stat-mech].