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.
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