This paper is concerned with the stochastic near‐optimal control problem for a regime‐switching diffusion model, where the control domains are convex. The controlled system is described by the Itô‐type stochastic differential equation (SDE) with a continuous‐time Markov chain, which possesses a finite state structure. Some new estimates for state and adjoint processes are obtained in the presence of the Markovian jumps. Based on these estimates and Ekeland's variational principle, the necessary and sufficient conditions for near‐optimality of this model are established. A numerical example is given to illustrate the effectiveness of theoretical results.

中文翻译：

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体制转换扩散模型中接近最优的充要条件

本文关注的是控制域为凸的政权切换扩散模型的随机近最优控制问题。受控系统由具有连续状态马尔可夫链的伊藤型随机微分方程（SDE）来描述，该链具有有限的状态结构。在存在马尔可夫跳跃的情况下，可以获得状态和伴随过程的一些新估计。基于这些估计和Ekeland的变分原理，建立了该模型接近最优的充要条件。数值例子说明了理论结果的有效性。