On arbitrarily varying Markov source coding and hypothesis LAO testing by non-informed statistician

Two problems concerning arbitrarily varying stationary Markov source (AVMS), namely, the binary hypothesis testing and the source coding problems are solved. First, we consider a logarithmically asymptotically optimal (LAO) hypothesis testing (HT) for distributions of AVMS. The asymptotic behavior of the second type error probability exponent is investigated in function of the first type error probability exponent, as the number of observations tends to infinity. In the problem of AVMS coding, the E-optimal rate function R(E) (the minimum rate R of the source sequences compression when the decoding error probability is less than exp{-NE}, (E > 0) and its inverse reliability function E(R) are obtained from the corresponding HT result.