论文标题
由SPDES控制的随机最佳控制问题通过时空相互作用算子
A stochastic optimal control problem governed by SPDEs via a spatial-temporal interaction operator
论文作者
论文摘要
在本文中，我们首先引入了一个新的时空相互作用算子来描述时空依赖性现象。然后，我们考虑由随机偏微分方程与时空相互作用算子控制的新系统的随机最佳控制。为了解决这样的随机最佳控制问题，我们通过定义哈密顿功能，从而得出具有空间依赖性的伴随随机偏微分方程，并提供了足够和必要的（Pontryagin-Bismut-Bessous-bessoussan型）最大原则。此外，对于相应的向后随机部分微分方程，证明了解决方案的存在和唯一性。最后，我们的结果用于研究与时空相关现象的人口增长问题。
In this paper, we first introduce a new spatial-temporal interaction operator to describe the space-time dependent phenomena. Then we consider the stochastic optimal control of a new system governed by a stochastic partial differential equation with the spatial-temporal interaction operator. To solve such a stochastic optimal control problem, we derive an adjoint backward stochastic partial differential equation with spatial-temporal dependence by defining a Hamiltonian functional, and give both the sufficient and necessary (Pontryagin-Bismut-Bensoussan type) maximum principles. Moreover, the existence and uniqueness of solutions are proved for the corresponding adjoint backward stochastic partial differential equations. Finally, our results are applied to study the population growth problems with the space-time dependent phenomena.
