2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121571Equipping the probability space with a local Dirichlet form with square field operator $Γ$ and generator $A$ allows to improve Monte Carlo computations of expectations, densities, and conditional expectations, as soon as we are able to simulate a random variable $X$ together with $Γ[X]$ and $A[X]$. We give examples on the Wiener space, on the Poisson space and on the Monte Carlo space. When $X$ is real-valued we give an explicit formula yielding the density at the speed of the law of large numbers.Probability31C25 60H07 65G99 65C05 65C20text