Necessary conditions for optimality for a diffusion with a non-smooth drift
Necessary conditions for optimality for a diffusion with a non-smooth drift
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非平滑漂移扩散最优的必要条件
DOI：
10.1080/17442508808833521
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
Mezerdi Brahim
中科院分区：
文献类型：
--
作者：
Mezerdi Brahim
本文的目的是在没有漂移的可微性假设的情况下，建立受控随机微分系统最优的必要条件。我们使用一个近似变元来得到一系列光滑的控制问题，并应用Ekeland的变分原理推导出相关的伴随过程。经过关于稳定收敛的极限，我们得到了一个弱伴随过程和哈密顿量之间的不等式。这一结果是库什纳最大值原理的推广
The purpose of this paper is to establish the necessary conditions for optimality of a controlled stochastic differential system without differentiability assumptions on the drift. We use an approximation argument in order to obtain a sequence of smooth control problems, and we apply Ekeland's variational principle to derive the associated adjoint processes. Passing at the Limit with respect to the stable convergence, we obtain a weak adjoint process and the inequality between Hamiltonians. This result is a generalisation of Kushner's maximum principle