无穷时域耗散系统的必要随机最大值原理
Necessary stochastic maximum principle for dissipative systems on infinite time horizon
摘要：
在多项式增长和联合单调性假设下，对无限水平上的有限维随机控制问题，建立了一个必要的随机最大值原理.第二个假设概括了通常的意义上，它是制定为一个联合条件的漂移和扩散项。主要的困难在于通过求解无界时间区间上的向后方程来构造一阶和二阶伴随过程。第一个伴随过程的特点是作为一个解决方案的一个落后的，这是良定感谢对偶参数。第二个可以通过另一个对偶关系来定义，该对偶关系用系统的哈密顿量和线性化的状态方程来表示。一些已知的模型验证联合单调性假设进行了讨论。
英文摘要：
We develop a necessary stochastic maximum principle for a finite-dimensional stochastic control problem in infinite horizon under a polynomial growth and joint monotonicity assumption on the coefficients. The second assumption generalizes the usual one in the sense that it is formulated as a joint condition for the drift and the diffusion term. The main difficulties concern the construction of the first and second order adjoint processes by solving backward equations on an unbounded time interval. The first adjoint process is characterized as a solution to a backward SDE, which is well-posed thanks to a duality argument. The second one can be defined via another duality relation written in terms of the Hamiltonian of the system and linearized state equation. Some known models verifying the joint monotonicity assumption are discussed as well.
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