  Equipping the probability space with a local Dirichlet form with square field
operator $\Gamma$ 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 $\Gamma[X]$ 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.
