Given an arbitrary long but finite sequence of observations from a finite set, we construct a simple process that approximates the sequence, in the sense that with high probability the empirical frequency, as well as the empirical one-step transitions along a realization from the approximating process, are close to that of the given sequence.
We generalize the result to the case where the one-step transitions are required to be in given polyhedra.
"Approximating a sequence of observations by a simple process." Ann. Statist. 32 (6) 2742 - 2775, December 2004. https://doi.org/10.1214/009053604000000643