Improving Monte Carlo simulations by Dirichlet forms
Nicolas Bouleau · Comptes Rendus Mathématique · 2005
Equipping the probability space with a local Dirichlet form with square field operator Γ and generator A allows us to improve Monte Carlo simulations of expectations and densities 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.