A variational representation for random functionals on abstract Wiener spaces

作者：Zhang Xicheng^*

来源：Journal of Mathematics of Kyoto University, 2009, 49(3): 475-490.

DOI：10.1215/kjm/1260975036

We extend to abstract Wiener spaces the variational representation
E[(F)(e)] = exp (sup(nu is an element of Ha) E [F(. nu) - 1/2 parallel to nu parallel to(2)(H)]),
proved by Boue and Dupuis [1] on the classical Wiener space. Here F is my bounded measurable function on the abstract Wiener space (W, H, mu), and H(a) denotes the space of F(t)-adapted H-valued random fields in the sense of Ustunel 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.

• 出版日期2009
• 单位华中科技大学