Measures of distinguishability between stochastic processes

Chengran Yang, Felix C. Binder, Mile Gu, Thomas J. Elliott

Research output: Contribution to journalArticlepeer-review


Quantifying how distinguishable two stochastic processes are is at the heart of many fields, such as machine learning and quantitative finance. While several measures have been proposed for this task, none have universal applicability and ease of use. In this article, we suggest a set of requirements for a well-behaved measure of process distinguishability. Moreover, we propose a family of measures, called divergence rates, that satisfy all of these requirements. Focusing on a particular member of this family—the coemission divergence rate—we show that it can be computed efficiently, behaves qualitatively similar to other commonly used measures in their regimes of applicability, and remains well behaved in scenarios where other measures break down.
Original languageEnglish
Article number062137
Number of pages12
JournalPhysical Review E
Issue number6
Publication statusPublished - 23 Jun 2020


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