Can we use perfect simulation for non-monotonic Markovian systems ?

International audienceSimulation approaches are alternative methods to estimate the stationary be- havior of stochastic systems by providing samples distributed according to the stationary distribution, even when it is impossible to compute this distribution numerically. Propp and Wilson used a backward coupling to derive a simu- lation algorithm providing perfect sampling (i.e. which distribution is exactly stationary) of the state of discrete time finite Markov chains. Here, we adapt their algorithm by showing that, under mild assumptions, backward coupling can be used over two simulation trajectories only