Stochastic Decision with Stationary Memoryless Sequence

This paper investigates a stochastic decision problem with a stationary memoryless random sequence of states, where the maximum a posteriori decision is employed within the states. We derive novel upper bounds on the decision error probability depending on the sequence length. It is shown that, when a sequence is generated subject to an a posteriori distribution, the ratio of the error probability divided by the error probability of the maximum a posteriori decision approaches one as the sequence length increases.