A variational representation for certain functionals of Brownian motion
A variational representation for certain functionals of Brownian motion
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DOI：
10.1214/aop/1022855876
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发表时间：
1998-10
影响因子：
2.3
通讯作者：
M. Boué;P. Dupuis
中科院分区：
文献类型：
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作者：
M. Boué;P. Dupuis
本文证明了变分表示- log Ee -f(W) = inf E{1/2∫0 1∥v s∥2 ds + f(W +∫0 v s ds)}成立，其中W是标准d维布朗运动，f是映射C([0,1]的任意有界可测函数：将R (d)分解为R，其最小值是在所有过程v上，这些过程v是相对于w产生的滤波的增大而逐渐可测量的。
In this paper we show that the variational representation - log Ee -f(W) = inf E{1/2∫ 0 1 ∥v s ∥ 2 ds + f(w + ∫ 0 v s ds)} holds, where W is a standard d-dimensional Brownian motion, f is any bounded measurable function that maps C([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 W. An application is made to a problem concerned with large deviations, and an extension to unbounded functions is given.