| 具有一般终端时刻和非一致线性增长生成元的倒向随机微分方程的$L^p$解 |
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| 引用本文： | 鹿高杰,江龙,李德鹏,范胜君.具有一般终端时刻和非一致线性增长生成元的倒向随机微分方程的$L^p$解[J].数学研究及应用,2016,36(1):117-126. |
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| 作者姓名： | 鹿高杰 江龙 李德鹏 范胜君 |
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| 作者单位： | 同济大学浙江学院数学教研室, 浙江 嘉兴 314000;中国矿业大学理学院, 江苏 徐州 221116;中国矿业大学理学院, 江苏 徐州 221116;中国矿业大学理学院, 江苏 徐州 221116 |
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| 基金项目： | 国家自然科学基金(Grant No.11371362), 中央高校基本科研业务费项目 (Grant No.2012LWB48). |
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| 摘 要： | In this paper, we establish the existence of the minimal L~p(p 1) solution of backward stochastic differential equations(BSDEs) where the time horizon may be finite or infinite and the generators have a non-uniformly linear growth with respect to t. The main idea is to construct a sequence of solutions {(Y~n, Z~n)} which is a Cauchy sequence in S~p× M~p space, and finally we prove {(Y~n, Z~n)} converges to the L~p(p 1) solution of BSDEs.
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| 关 键 词： | 倒向随机微分方程 有限或无限终端时刻 非一致线性增长生成元 Cauchy列 $L^p~(p>1)$解 |
| 收稿时间： | 2014/10/18 0:00:00 |
| 修稿时间： | 9/2/2015 12:00:00 AM |
$L^p$ Solutions of BSDEs with Non-Uniformly Linear Growth Generators and General Time Interval |
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| Gaojie LU,Long JIANG,Depeng LI and Shengjun FAN.$L^p$ Solutions of BSDEs with Non-Uniformly Linear Growth Generators and General Time Interval[J].Journal of Mathematical Research with Applications,2016,36(1):117-126. |
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| Authors: | Gaojie LU Long JIANG Depeng LI and Shengjun FAN |
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| Institution: | Department of Mathematics, Tongji Zhejiang College, Zhejiang 314000, P. R. China;School of Sciences, China University of Mining and Technology, Jiangsu 221116, P. R. China;School of Sciences, China University of Mining and Technology, Jiangsu 221116, P. R. China;School of Sciences, China University of Mining and Technology, Jiangsu 221116, P. R. China |
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| Abstract: | In this paper, we establish the existence of the minimal $L^p~(p>1)$ solution of backward stochastic differential equations (BSDEs) where the time horizon may be finite or infinite and the generators have a non-uniformly linear growth with respect to $t$. The main idea is to construct a sequence of solutions $\{(Y^n,Z^n)\}$ which is a Cauchy sequence in $\mathbb{S}^{p} \times \mathbb{M}^{p}$ space, and finally we prove $\{(Y^n,Z^n)\}$ converges to the $L^p~(p>1)$ solution of BSDEs. |
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| Keywords: | BSDEs finite or infinite time interval non-uniformly linear growth generators Cauchy sequence $L^p~(p>1)$ solutions |
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