Hypothesis Testing for Arbitrarily Varying Source

Hypothesis testing for arbitrarily varying source (AVS), which is to decide between the two hypothesis for varying behavior of the distribution of AVS, is considered in this paper. We determinate the best asymptotic exponent of the second kid of error probability when the first kind of error probability of fixed. This result generalized the well-known lemma of Stein in statistics. As a corollary, Strassens's coding theorem for AVS is obtained.