Dirichlet forms methods, an application to the propagation of the error due to the Euler scheme

Nicolas Bouleau (1)

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

We present recent advances on Dirichlet forms methods either to extend financial models beyond the usual stochastic calculus or to study stochastic models with less classical tools. In this spirit, we interpret the asymptotic error on the solution of an sde due to the Euler scheme in terms of a Dirichlet form on the Wiener space, what allows to propagate this error thanks to functional calculus.

Mots clés: squared field operator; Wiener space; density; Dirichlet process; stochastic differential equation; Dirichlet form; error

Domaines: Probabilités [math.PR]

Nicolas Bouleau. Dirichlet forms methods, an application to the propagation of the error due to the Euler scheme. 2006. ⟨hal-00106722⟩