A variational representation for random functionals on abstract Wiener spaces

We extend to abstract Wiener spaces the variational representation E[e ^F] = exp (supv E[F(-+V) -||v\\²H]) , proved by Boue and Dupuis [1] on the classical Wiener space. Here F is any bounded measurable function on the abstract Wiener space (W, H,), and H^a denotes the space of .F_t-adapted H-valued random fields in the sense of Ustiinel and Zakai [11]. In particular, we simplify the proof of the lower bound given in [1, 3] by using the Clark-Ocone formula. As an application, a uniform Laplace principle is established.