Informational and Causal Architecture of Continuous-time Renewal and Hidden Semi-Markov Processes

Abstract

We introduce the minimal maximally predictive models (ε-machines) of processes generated by certain hidden semi-Markov models. Their causal states are either hybrid discrete-continuous or continuous random variables and causal-state transitions are described by partial differential equations. Closed-form expressions are given for statistical complexities, excess entropies, and differential information anatomy rates. We present a complete analysis of the ε-machines of continuous-time renewal processes and, then, extend this to processes generated by unifilar hidden semi-Markov models and semi-Markov models. Our information-theoretic analysis leads to new expressions for the entropy rate and the rates of related information measures for these very general continuous-time process classes.

16 pages, 7 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/ctrp.htm

References in corpus (3)

• Structure and Randomness of Continuous-Time Discrete-Event Processes
• Information Anatomy of Stochastic Equilibria
• Statistical Signatures of Structural Organization: The case of long memory in renewal processes

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