Structure and Randomness of
Continuous-Time Discrete-Event 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: Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical complexity of stochastic processes generated by finite unifilar hidden semi-Markov models—memoryful, state-dependent versions of renewal processes. Calculating these quantities requires introducing novel mathematical objects (ε-machines of hidden semi-Markov processes) and new information-theoretic methods to stochastic processes.

Sarah Marzen and James P. Crutchfield, "Structure and Randomness of Continuous-time, Discrete-event Processes", Journal of Statistical Physis 169:2 (2017) 303-315.
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Santa Fe Institute Working Paper 17-04-009. [cond-mat.stat-mech].