Biological application of optimal stopping time problem (Q2263750)

Summary: In this paper, we develop some extensions of results proposed by \textit{S. Dayanik} and \textit{I. Karatzas} [Stochastic Processes Appl. 107, No. 2, 173--212 (2003; Zbl 1075.60524)] on optimal stopping time problem, and apply them to the Wright-Fisher diffusion process. In this respect, we study in details the important problem of boundary behaviour of the diffusion that approximates the Markov chain. As application, we find the perfect time to turn off the monitor genetic diseases. Precisely, we find the optimal stopping time at which is maximised the probability that a sample of size n, taken from large infected population, consists only of uninfected individuals. We show that this maximal probability is nothing other than the probability of fixation of the infected allele in case of bounded scale function.