Acta mathematica scientia, Series B >
INVARIANT REPRESENTATION FOR STOCHASTIC DIFFERENTIAL OPERATOR BY BSDES WITH UNIFORMLY CONTINUOUS COEFFICIENTS AND ITS APPLICATIONS
Received date: 2011-08-31
Revised date: 2012-02-22
Online published: 2013-09-20
Supported by
The authors thank the partial support from the NSF of China (11171186), the NSF of Shandong Province(ZR2010AM021) and the “111” project.
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 continu-ous 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 so-lutions of BSDEs. Moreover, we give a new proof about g-convexity.
JIA Guang-Yan , ZHANG Na . INVARIANT REPRESENTATION FOR STOCHASTIC DIFFERENTIAL OPERATOR BY BSDES WITH UNIFORMLY CONTINUOUS COEFFICIENTS AND ITS APPLICATIONS[J]. Acta mathematica scientia, Series B, 2013 , 33(5) : 1407 -1418 . DOI: 10.1016/S0252-9602(13)60092-2
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