A variational representation for random functionals on abstract Wiener spaces (Q965067)

The authors extend a variational representation for the Laplace transform \(E(e^F)\) of a bounded measurable functional \(F\) of classical Brownian motion due to \textit{M. Boue} and \textit{P. Dupois} [Ann. Probab. 26, No.~4, 1641--1659 (1998; Zbl 0935.60059)] by taking a bounded measurable function \(F\) on the abstract Wiener space. The authors here work with random fields in the sense of Üstünel and Zakai and use the Clark-Ocone formula in order to derive the lower bound in the representation. As an application, a uniform Laplace principle is established.