Large-deviation theorems in hypothesis-testing problems

Large-deviation theorems of Chernoff type for the logarithm of the likelihood ratio in general binary statistical experiments are obtained. The obtained limit theorems are used to investigate of the rate of decrease of the error probabilities for Neyman-Pearson tests, Bayes tests, and minimax tests in statistical experiments generated by normal autoregressive processes and Galton-Watson processes with immigration. Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part II.