Sequential Testing of Two Hypotheses for a Stationary Ornstein--Uhlenbeck Process

The present paper is concerned with the conditionally extremal settings of the sequential testing problem of two simple hypotheses about a parameter responsible for the local return rate of a stationary Ornstein--Uhlenbeck process to its mean value. Minimization of the Kullback--Leibler divergence is considered as an optimality test. An asymptotically optimal scheme is put forward, first, in the case when the error probabilities of the first and the second kind tend to zero, and, second, in the case when the tested parameters go off to infinity but the distance between them is fixed.