| 基于g期望的二元Jensen不等式 |
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| 引用本文： | 徐玉红,刘玉春,高杰.基于g期望的二元Jensen不等式[J].黑龙江科技学院学报,2007,17(3):224-226,230. |
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| 作者姓名： | 徐玉红 刘玉春 高杰 |
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| 作者单位： | 中国矿业大学,理学院,江苏,徐州,221008 |
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| 摘 要： | 利用Girsanov变换,证明了当g是线性生成元时,g期望等价于经典的数学期望,此时,g期望关于一般二元凹函数的Jensen不等式成立,然后采用生成元表示定理,得到了若g期望关于一般二元凹函数的Jensen不等式成立,则生成元是线性的;最后证明了当且仅当g是次线性生成元时,g期望关于二元单调递增凹函数的Jensen不等式成立.
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| 关 键 词： | 倒向随机微分方程 g期望 Jensen不等式 数学期望 Jensen 不等式 g expectation function bivariate 单调递增 次线性 表示定理 凹函数 生成元 变换 Girsanov 利用 |
| 文章编号： | 1671-0118（2007）03-0224-03 |
| 修稿时间： | 2007-03-16 |
Jensen's inequality of bivariate function for g expectation |
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| XU Yuhong,LIU Yuchun,GAO Jie.Jensen''''s inequality of bivariate function for g expectation[J].Journal of Heilongjiang Institute of Science and Technology,2007,17(3):224-226,230. |
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| Authors: | XU Yuhong LIU Yuchun GAO Jie |
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| Institution: | College of Science, China University of Mining and Technology, Xuzhou 221008, China |
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| Abstract: | Using Girsanov transformation,the paper presents an attempt to prove that g expectation is equal to the classical expectation when g is a linear generator,thus Jensen's inequality of general bivariate concave function for g expectation holds.Then the paper,by exploring the representation theorem for generators,leads to conclusion that g is linear when Jensen's inequality of general bivariate concave function holds;it is proved that Jensen's inequality of bivariate increasing concave function holds if and only if g is a sublinear generator. |
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| Keywords: | backward stochastic differential equation(BSDE) g expectation Jensen inequality |
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