2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138643The target measure $μ$ is the distribution of a random vector in a box $\cB$, a Cartesian product of bounded intervals. The Gibbs sampler is a Markov chain with invariant measure $μ$. A ``coupling from the past'' construction of the Gibbs sampler is used to show ergodicity of the dynamics and to perfectly simulate $μ$. An algorithm to sample vectors with multinormal distribution truncated to $\cB$ is then implemented.22 pages, submitted to Journal of Applied ProbabilityProbabilityStatistics Theory60G15, 60G10, 65C05text