SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 953-981, April 2024.
Abstract. In this paper, we study optimal stochastic control problems for stochastic systems driven by non-Markov subdiffusion [math], which have mixed features of deterministic and stochastic controls. Here [math] is the standard Brownian motion on [math], and [math] is the inverse of a subordinator [math] with drift [math] that is independent of [math]. We obtain stochastic maximum principles (SMPs) for these systems using both convex and spiking variational methods, depending on whether or not the domain is convex. To derive SMPs, we first establish a martingale representation theorem for subdiffusions [math], and then use it to derive the existence and uniqueness result for the solutions of backward stochastic differential equations (BSDEs) driven by subdiffusions, which may be of independent interest. We also derive sufficient SMPs. Application to a linear quadratic system is given to illustrate the main results of this paper.

中文翻译：

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次扩散的随机极大值原理及其应用

SIAM 控制与优化杂志，第 62 卷，第 2 期，第 953-981 页，2024 年 4 月。
摘要。在本文中，我们研究由非马尔可夫子扩散[数学]驱动的随机系统的最优随机控制问题，该系统具有确定性和随机控制的混合特征。这里 [math] 是 [math] 上的标准布朗运动，[math] 是具有独立于 [math] 的漂移 [math] 的从属子 [math] 的逆。我们使用凸变分法和尖峰变分法获得这些系统的随机最大原理（SMP），具体取决于域是否是凸的。为了推导SMP，我们首先建立子扩散的鞅表示定理[数学]，然后用它推导子扩散驱动的后向随机微分方程（BSDE）解的存在性和唯一性结果，这可能是独立的兴趣。我们还获得了足够的 SMP。给出了在线性二次系统中的应用来说明本文的主要结果。