Optimal adaptive sampling for a symmetric two-state continuous time Markov chain

We consider the optimal sampling times for a symmetric two-state continuous time Markov chain. We first consider sampling times of the form ti=i. and find the optimal . to minimize the asymptotic variance of our estimated parameter. This optimal . depends upon the true unknown parameters and so it is infeasible in practice. To address this, we consider propose an adaptive scheme which we requires no knowledge of the true underlying parameter, we show that this method is asymptotically equivalent to the optimal fixed time design.