Editing Markov chain (section)

===Bernoulli scheme===
{{Main|Bernoulli scheme}}
A [[Bernoulli scheme]] is a special case of a Markov chain where the transition probability matrix has identical rows, which means that the next state is independent of even the current state (in addition to being independent of the past states). A Bernoulli scheme with only two possible states is known as a [[Bernoulli process]].

Note, however, by the [[Ornstein isomorphism theorem]], that every aperiodic and irreducible Markov chain is isomorphic to a Bernoulli scheme;<ref name="nicol">
Matthew Nicol and Karl Petersen, (2009) "[https://www.math.uh.edu/~nicol/pdffiles/petersen.pdf Ergodic Theory: Basic Examples and Constructions]",
''Encyclopedia of Complexity and Systems Science'', Springer https://doi.org/10.1007/978-0-387-30440-3_177
</ref> thus, one might equally claim that Markov chains are a "special case" of Bernoulli schemes. The isomorphism generally requires a complicated recoding. The isomorphism theorem is even a bit stronger: it states that ''any'' [[stationary stochastic process]] is isomorphic to a Bernoulli scheme; the Markov chain is just one such example.