| 范胜君,江龙.生成元一致连续的多维倒向随机微分方程的$L^p$解[J].数学年刊A辑,2013,34(6):761~770 |
| 生成元一致连续的多维倒向随机微分方程的$L^p$解 |
| $L^p$Solutions to Multidimensional Backward Stochastic Differential Equations withUniformly Continuous Generators |
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| DOI： |
| 中文关键词: 倒向随机微分方程, 一致连续生成元, 存在唯一性,
$L^p$~解 |
| 英文关键词:Backward stochastic differential equation, Uniformly continuous generator, Existence and uniqueness, $L^p$ solution |
| 基金项目:国家自然科学基金(No.11101422), 中央高校基础研究基金(No.2012QNA36)和江苏省青蓝工程中青年学术带头人培养对象专项基金(No.苏教师[2012]39号) |
| Author Name | Affiliation | E-mail | | FAN Shengjun | School of Mathematical Sciences, Fudan University, Shanghai 200433, China
College of Sciences, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China. | fsj@126.com | | JIANG Long | College of Sciences, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China. | jianglong365@hotmail.com |
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| 中文摘要: |
| 在生成元~$g$~的第~$i$~个分量~$g_i(t,y,z)$~仅仅依赖于矩阵~$z$~的第~$i$
行的条件下, Hamad\`{e}ne于2003年证明了生成元一致连续的倒向随机微分
方程的~$L^2$~解的存在性, 其~$L^2$~解的唯一性由范胜君等于2010年得到. 本文进一步地证明了该类倒向随机微分
方程的~$L^p\ (p>1)$~解的存在唯一性. |
| 英文摘要: |
| In 2003, Hamad\`{e}ne proved the existence of $L^2$ solutions to multidimensional backward stochastic
differential equations (or BSDEs for short) with uniformly continuous generators,
provided that the $i$th component $g_i(t,y,z)$ of the generator $g$ depends only on the
$i$th row of the matrix $z$. The uniqueness of $L^2$ solutions was obtained by Fan et al. in 2010.
In this paper, the authors further prove the existence and uniqueness of $L^p\ (p>1)$ solutions to this kind of BSDEs. |
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