2016/06/02 by Gurevich, Boris
#37A35 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1606.00584
Many years ago B.S. Pitskel observed that the metric entropy of the shift transformation in the sample space of a stationary random process X=\Xn, n∈ \mathbb Z\ with a countable number of states is equal to the conditional entropy H(X0|X-1,X-2,…) if X is a stationary Markov chain (in which case the above conditional entropy is H(X0|X-1)), whether the entropy H(X0) is finite or not, while in general the statement is not true. In this note we present a class of processes for which Pitskel's observation holds, despite the fact that no of these processes is a Markov chain of some order.