INVARIANT REPRESENTATION FOR STOCHASTIC DIFFERENTIAL OPERATOR BY BSDES WITH UNIFORMLY CONTINUOUS COEFFICIENTS AND ITS APPLICATIONS  

作　　者：贾广岩 张娜 

机构地区：[1]Qilu Securities Institute for Financial Studies, Shandong University [2]College of Management and Economics, Tianjin University [3]China Center for Social Computing, Tianjin University

出　　处：《Acta Mathematica Scientia》2013年第5期1407-1418,共12页数学物理学报（B辑英文版）

基　　金：the partial support from the NSF of China(11171186);the NSF of Shandong Province(ZR2010AM021);the "111" project

摘　　要：In this paper, we prove that a kind of second order stochastic differential op- erator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of the representation for the uniformly continuous generator. With the help of this representation, we obtain the corresponding converse comparison theorem for the BSDEs with uniformly continuous coefficients, and get some equivalent relationships between the properties of the generator g and the associated solutions of BSDEs. Moreover, we give a new proof about g-convexity.In this paper, we prove that a kind of second order stochastic differential op- erator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of the representation for the uniformly continuous generator. With the help of this representation, we obtain the corresponding converse comparison theorem for the BSDEs with uniformly continuous coefficients, and get some equivalent relationships between the properties of the generator g and the associated solutions of BSDEs. Moreover, we give a new proof about g-convexity.

关 键 词：backward stochastic differential equations stochastic differential operators representation theorems converse comparison theorem 

分 类 号：O211.63[理学—概率论与数理统计] O175.1[理学—数学]