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## Section: Software and Platforms

### $\psi$ and ${\psi }^{2}$: perfect simulation of Markov Chain stationary distributions

Participant : Jean-Marc Vincent [correspondent] .

$\psi$ and ${\psi }^{2}$ (see http://psi.gforge.inria.fr ) are two software tools implementing perfect simulation of Markov Chain stationary distributions using coupling from the past. $\psi$ starts from the transition kernel to derive the simulation program while ${\psi }^{2}$ uses a monotone constructive definition of a Markov chain.