  A stochastic process that arises by composing a function with a Markov
process is called an aggregated Markov process (AMP). The purpose of composing
a Markov process with a function can be a reduction of dimensions, e.g., a
projection onto certain coordinates. The theory around AMP has been extensively
studied e.g. by Dynkin, Cameron, Rogers and Pitman, and Kelly, all of whom
provided sufficient conditions for an AMP to remain Markov. In another
direction, Larget provided a canonical representation for AMP, which can be
used to verify the equivalence of two AMPs. The purpose of this paper is to
describe how the theory of AMP can be applied to stochastic learning theory as
they learn a particular task.
