On Effective Computation of Expectations in Large or Infinite Dimension

Nicolas Bouleau (1)

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

This study is an analysis of the natural difficulties of integration by Monte Carlo or quasi-Monte Carlo methods. In spite of what is sometimes written, these methods work only in some precise cases. For the important problem of the computation of expectations of functionals of stochastic processes, we present the advantages of a method based on the implementation of the Bernoulli shift operator by pointers.

Mots clés: Monte Carlo; quasi-Monte Carlo; Riemann integrable; discrepancy; effectivity; infinite dimension; Bernoulli shift; pointer

Domaines: Probabilités [math.PR]; Analyse numérique [math.NA]

Nicolas Bouleau. On Effective Computation of Expectations in Large or Infinite Dimension. Journal of Computational and Applied Mathematics, 1990, 31, pp.23-34. ⟨hal-00448696⟩