Informational and Causal Architecture of Continuous-time Renewal Processes
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Author(s)
Crutchfield, James P.
Marzen, Sarah E.
Date Issued
April 2017
Journal
Journal of Statistical Physics
Publisher
Springer US
Citation
Marzen, Sarah, and James P. Crutchfield. “Informational and Causal Architecture of Continuous-Time Renewal Processes.” Journal of Statistical Physics 168.1 (2017): 109–127.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10955-017-1793-z
