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A short introduction to observable operator models of stochastic processes

The article describes a new formal approach to model discrete stochastic processes, called observable operator models (OOMs). It is shown how hidden Markov models (HMMs) can be properly generalized to OOMs. These OOMs afiord both mathematical simplicity and algorithmic e‐ciency, where HMMs exhibit neither. The observable operator idea also leads to an abstract, information-theoretic representation of stationary stochastic processes. It is shown how any such process can be uniquely characterized by linear, observable operators, yielding an abstract OOM of the process. All in all, observable operators open a lucid, general, and computationally extremely powerful avenue to stochastic processes.