Central limit theorem for the estimator of the value of an optimal stopping problem

We consider an optimal stopping problem defined on a finite Markov chain whose transition probabilities are unknown. We prove a central limit theorem for the maximum likelihood estimator and the stretch estimator of the optimal value of the optimal stopping problem. Also, we propose a perturbation technique to weaken the hypotheses of the central limit theorem. The author was supported by a grant from the SpanishScretaría de Estado de Educación y Universidades in cooperation with the European Social Funds.