| 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,2020,41(4):409~428 |
| 平均场倒向重随机微分方程及其应用 |
| Mean-Field Backward Doubly Stochastic Differential Equations and Its Applications |
| 投稿时间：2018-11-17 修订日期：2020-08-10 |
| DOI：10.16205/j.cnki.cama.2020.0029 |
| 中文关键词: 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 |
| 英文关键词:Mean-Field, Backward doubly stochastic differential equations,Nonlocal stochastic partial differential equations, Maximum principle, Linear quadratic optimal control |
| 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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| 中文摘要: |
| 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. |
| 英文摘要: |
| In this paper, mean-field backward doubly stochastic differential equations (MFBDSDEs in short) are introduced and studied. The existence and uniqueness of solutions for MF-BDSDEs is established. One probabilistic interpretation for the solutions to a class of nonlocal stochastic partial differential equations is given. A maximum principle of Pontryagin’s type is established for optimal control problems of MF-BDSDEs. Finally, one backward linear quadratic optimal control problem of mean-field type is discussed to illustrate the direct application of the maximum principle. |
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