Cutoff time based on generalized divergence measure

The cutoff phenomenon in the simulated methods has been widely investigated in recent years. An important question is to detect the stopping time after which one can obtain the convergence to equilibrium of an interesting Markov chain. We propose in this paper, a method for evaluating the cutoff instant using appropriate stopping times such as those found in [Lachaud, B. 2005. Cutoff and hitting times for a sample of Ornstein-Uhlenbeck processes and its everage, J. Appl. Probab. 42 (4), 1069-1080]. We give the conditions under which a Markov process has a cutoff time, in the sense of the generalized divergence measure. For illustration, we evaluate the effectiveness of our method on the Ornstein-Uhlenbeck process.