Mean field approach to stochastic control with partial information
Mean field approach to stochastic control with partial information
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DOI：
10.1051/cocv/2021085
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发表时间：
2021-08-24
影响因子：
1.4
通讯作者：
Yam, Sheung Chi Phillip
中科院分区：
文献类型：
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作者：
Bensoussan, Alain;Yam, Sheung Chi Phillip
在我们的这篇文章中，我们沿着我们早期工作中的平均场类型控制理论的发展道路[Bensoussan等人，平均场游戏和平均场类型控制理论]。Springer，New York(2013)]，首先介绍了Bellman方程，然后介绍了Hamilton-Jacobi-Bellman(HJB)和Fokker-Planck(FP)方程组，然后通过寻找线性二次情形的半显式解来处理它们，特别是在任意初始分布的情况下；这样的问题被长期搁置，在早期的文献中没有被具体处理，如Bensoussan[部分可观测系统的随机控制]。剑桥大学出版社，(1992)和Nisio[随机控制理论：动态规划原理]。Springer(2014)]，它只处理了具有高斯初始分布的线性二次设置。由于有效平均场理论，我们提出了一个解决这个长期存在的问题的一般非高斯情况。此外，我们在这里考虑的问题可以归结为Bandini等人的模型。[随机过程。APPL129(2019)674-711]，这与我们目前拟议的框架有根本的不同。
In our present article, we follow our way of developing mean field type control theory in our earlier works [Bensoussan et al., Mean Field Games and Mean Field Type Control Theory. Springer, New York (2013)], by first introducing the Bellman and then master equations, the system of Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck (FP) equations, and then tackling them by looking for the semi-explicit solution for the linear quadratic case, especially with an arbitrary initial distribution; such a problem, being left open for long, has not been specifically dealt with in the earlier literature, such as Bensoussan [Stochastic Control of Partially Observable Systems. Cambridge University Press, (1992)] and Nisio [Stochastic control theory: Dynamic programming principle. Springer (2014)], which only tackled the linear quadratic setting with Gaussian initial distributions. Thanks to the effective mean-field theory, we propose a solution to this long standing problem of the general non-Gaussian case. Besides, our problem considered here can be reduced to the model in Bandini et al. [Stochastic Process. Appl. 129 (2019) 674-711], which is fundamentally different from our present proposed framework.