On the converse theorem in statistical hypothesis testing for Markov chains

Abstract

Hypothesis testing for two Markov chains is considered. Under the constraint that the error probability of the first kind is less than or equal to exp(-rn), the error probability of the second kind is minimized. The geodesic that connects the two Markov chains is defined. By analyzing the geodesic, the power exponents are calculated and then represented in terms of Kullback-Leibler divergence.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>