Notes on Finitary Isomorphism Markers in Countable State Markov Processes
2012, v.18, №2, 323-332
In 1979, Keane and Smorodinsky showed that entropy is a complete finitary isomorphism invariant for Bernoulli schemes. The first and perhaps most crucial step in their proof was to find markers. In 1982, Rudolph showed that entropy is a complete finitary isomorphism invariant for countable state Markov chains with exponentially decaying return times. However, he did not use the same methods as Keane and Smorodinsky, leaving open the question of whether the Keane and Smorodinsky methods could be extended to these types of processes. Here, we show how the Keane and Smorodinsky methods can be extended to certain countable state Markov chains.
Keywords: Bernoulli scheme,Markov,r-process,finitary isomorphism