Improving Monte Carlo simulations by Dirichlet forms

Nicolas Bouleau (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

Equipping the probability space with a local Dirichlet form with square field operator Γ and generator A allows 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.

Mots clés: Monte Carlo; Dirichlet form; carré du champ; square field operator; generator; sumulation

Domaines: Probabilités [math.PR]

Nicolas Bouleau. Improving Monte Carlo simulations by Dirichlet forms. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2005, 341, pp.303-306. ⟨hal-00781404⟩