倒向随机微分方程第二部分解的比较定理  

Comparison theorem for second part of solutions to BSDEs

作　　者：徐玉红 刘玉春[2] 

机构地区：[1]炎黄大学数学系,江苏淮安223400 [2]南开大学滨海学院应用数学系,天津300270

出　　处：《黑龙江科技学院学报》2009年第2期147-149,153,共4页Journal of Heilongjiang Institute of Science and Technology

摘　　要：为研究倒向随机微分方程第二部分解的比较性质,利用倒向随机微分方程解的Malli-avin微分,第二部分解可化为一个线性倒向随机微分方程的第一部分解,再结合经典的比较定理,给出第二部分解的比较定理成立的一个充分条件。通过该比较定理,可以把第二部分解控制在一个确定的闭区间,并由此指出一类可以退化为常微分方程的倒向随机微分方程。Aimed at investigating the property of comparisons for the second part of solutions to backward stochastic differential equations （BSDEs）, this paper introduces the use of Malliavin calculus on BSDEs to convert the second part of solutions to the first part of solutions to a linear BSDE and combine the classical comparison theorem to give a sufficient condition under which the comparison theorem for the second part of solutions to BSDEs holds. The comparison theorem allows the second part of solutions to BSDEs to be controlled within a closed deterministic interval so that a class of BSDEs are specified to be ordinary differential equations.

关 键 词：倒向随机微分方程 比较定理 控制定理 

分 类 号：O211.63[理学—概率论与数理统计]