Abstract
Equipping 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.