A new approach to the martingale representation theorem

被引:4
作者
Fitzsimmons, P. J. [2 ]
Rajeev, B. [1 ]
机构
[1] Indian Stat Inst, Bangalore Ctr, Bangalore, Karnataka, India
[2] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA
来源
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC REPORTS | 2009年 / 81卷 / 05期
关键词
stochastic integral representation; martingale representation; Sobolev space; stochastic Sobolev space; conditional expectations; Wiener functionals;
D O I
10.1080/17442500802343417
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We prove the martingale representation theorem for Brownian motion, with an explicit expression for the integrand for random variables of the form f(1)(W-t1)f(2)(W-t2)center dot center dot center dot f(n)(W-tn). We introduce a new stochastic Sobolev space and reformulate the martingale representation theorem in terms of elements from this space.
引用
收藏
页码:467 / 476
页数:10
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