TY - JOUR
T1 - A variational representation for random functionals on abstract Wiener spaces
AU - Zhang, Xicheng
PY - 2009
Y1 - 2009
N2 - 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 Ha denotes the space of .Ft-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.
AB - 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 Ha denotes the space of .Ft-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.
UR - http://www.scopus.com/inward/record.url?scp=70450223930&partnerID=8YFLogxK
U2 - 10.1215/kjm/1260975036
DO - 10.1215/kjm/1260975036
M3 - Article
AN - SCOPUS:70450223930
SN - 2156-2261
VL - 49
SP - 475
EP - 490
JO - Kyoto Journal of Mathematics
JF - Kyoto Journal of Mathematics
IS - 3
ER -