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Open Access Publications from the University of California

Informational and Causal Architecture of Continuous-time Renewal Processes

  • Author(s): Marzen, S
  • Crutchfield, JP
  • et al.

© 2017, Springer Science+Business Media New York. 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.

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