Process Approximation and Metrics



The goodness or badness of approximation of one process for another can be quantified using various metrics (or distances) or distortion measures (or cost functions). Two of the most useful such notions of approximation are introduced and studied in this chapter — the distributional distance and the \(\bar{d}_p\) distortion. The former leads to a useful metric space of probability measures. The second combines ideas from the Monge/Kantorovich optimal transportation cost and Ornstein’s \(\bar{d}\) (dbar) distance on random variables, vectors, and processes and is useful for quantifying the different time-average behavior of frequency-typical or frequency-typical sequences produced by distinct random processes.


Probability Measure Polish Space Process Distribution Transportation Distance Distortion Measure 
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Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  1. 1.Department of Electrical EngineeringStanford UniversityStanfordUSA

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