Informational and Causal Architecture of Continuous-time Renewal Processes

Sarah Marzen, James P. Crutchfield
2017 Journal of statistical physics  
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
more » ... esses 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.
doi:10.1007/s10955-017-1793-z fatcat:6deeel5vyfhd5pfr3or3wnrn5y