| 平均场倒向重随机微分方程及其应用 |
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| 引用本文： | 朱庆峰,王天啸,石玉峰.平均场倒向重随机微分方程及其应用[J].数学年刊A辑(中文版),2020,41(4):409-428. |
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| 作者姓名： | 朱庆峰 王天啸 石玉峰 |
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| 作者单位： | 山东财经大学数学与数量经济学院, 山东省区块链金融重点实验室, 济南 250014;山东大学金融研究院和数学学院, 济南 250100.;四川大学数学学院, 成都 610065. |
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| 基金项目： | 国家重点研发计划 (No.2018YFA0703900), 国家自然科学基金(No.11871309, No.11671229, No.11971332, No.11931011, No.71871129, No.11371226, No.11301298),山东省自然科学基金 (No.ZR2019MA013), 山东省高等教育科技计划项目(No.J17KA162)和泰山学者工程专项经费(No.tsqn20161041) |
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| 摘 要： | 研究了平均场倒向随重机微分方程, 得到了平均场倒向重随机微分方程解的存在唯一性.基于平均场倒向重随机微分方程的解, 给出了一类非局部随机偏微分方程解的概率解释.讨论了平均场倒向重随机系统的最优控制问题, 建立了庞特利亚金型的最大值原理.最后讨论了一个平均场倒向重随机线性二次最优控制问题, 展示了上述最大值原理的应用.
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| 关 键 词： | 平均场 倒向重随机微分方程 非局部随机偏微分方程 最大值原理 线性二次最优控制 |
| 收稿时间： | 2018/11/17 0:00:00 |
| 修稿时间： | 2020/8/10 0:00:00 |
Mean-Field Backward Doubly Stochastic Differential Equations and Its Applications |
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| ZHU Qingfeng,WANG Tianxiao,SHI Yufeng.Mean-Field Backward Doubly Stochastic Differential Equations and Its Applications[J].Chinese Annals of Mathematics,2020,41(4):409-428. |
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| Authors: | ZHU Qingfeng WANG Tianxiao SHI Yufeng |
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| Institution: | School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Shandong Key Laboratory of Blockchain Finance, Jinan 250014, China;Institute for Financial Studies and School of Mathematics, Shandong University, Jinan 250100, China.;School of Mathematics, Sichuan University, Chengdu 610065, China.; Corresponding author. Institute for Financial Studies and School of Mathematics, Shandong University, Jinan 250100, China. |
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| Abstract: | Hom-Lie algebra is an anticommutative algebra with a multiplication such that the Hom-Jacobi identity holds. The twisted Heisenberg-Virasoro algebra L is the universal central extension of the Lie algebra W of differential operators of order at most one, which is connected with certain moduli spaces of curves. This paper mainly determines all Hom-Lie algebra structures on the twisted Heisenberg-Virasoro algebra L and gets some nontrivial Hom-Lie algebra structures on L. |
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| Keywords: | Mean-Field Backward doubly stochastic differential equations Nonlocal stochastic partial differential equations Maximum principle Linear quadratic optimal control |
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