A variational representation for certain functionals of Brownian motion

被引：3
|
作者：
Boué, M [1 ]
Dupuis, P
机构：
[1] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA
[2] Brown Univ, Div Appl Math, Lefschetz Ctr Dynam Syst, Providence, RI 02912 USA
来源：
ANNALS OF PROBABILITY | 1998年 / 26卷 / 04期
关键词：
variational representation; Brownian motion; large deviations; relative entropy;
D O I：
暂无
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In this paper we show that the variational representation -log Ee(-f(W)) = inf(v) E{1/2 integral(0)(1)//vs//(2) ds + f(W + integral(0)(.) vs ds)} holds, where W is a standard d-dimensional Brownian motion, f is any bounded measurable function that maps E([0,1]: R-d) into R and the infimum is over all processes v that are progressively measurable with respect to the augmentation of the filtration generated by FV. An application is made to a problem concerned with large deviations, and an extension to unbounded functions is given.
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页码：1641 / 1659
页数：19
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