Construction of Dirichlet structures

Nicolas Bouleau (1)

1 LAMM - Laboratoire de Mathématiques et Modélisation

We show how the construction of Dirichlet structures allow to equip the main probabilistic objects with Dirichlet forms. We emphasize the case of local white Dirichlet structures on the Poisson space and on the Wiener space. This yields tools for studying the existence of densities of functionals of processes.

Keywords: Dirichlet forms; Malliavin calculus; Poisson point process

Domains: Probability [math.PR]; Functional Analysis [math.FA]

Nicolas Bouleau. Construction of Dirichlet structures. 1996, pp.9-26. ⟨hal-00017931⟩