具有不可控扩散的G-中立型随机微分方程松弛最优控制的存在性
Existence of relaxed optimal control for G-neutral stochastic functional differential equations with uncontrolled diffusion
摘要：
本文研究了巴拿赫空间中由G-布朗运动驱动的中立型随机泛函微分方程（简称GNSFDEs）解的存在唯一性问题，其中中立项和扩散不依赖于控制变量.通过使用紧性技术和弱收敛技术，我们的动态的所有可能的概率的集合中的每个概率测度，我们证明了最优松弛控制的存在性。给出了研究的动机，并对非受控G-NSFDE进行了数值分析。
英文摘要：
In this paper, we study the question of existence and uniqueness of solution of neutral stochastic functional differential equations driven by G- Brownian motion (GNSFDEs in short) on Banach space driven by relaxed controls in which the neutral term and diffusion do not depend on the control variable. By using tightness techniques and the weak convergence techniques for each probability measure in the set of all possible probabilities of our dynamic, we prove the existence of an optimal relaxed control. A motivation of are work is presented and a Numerical analysis for the uncontrolled G-NSFDE is given.
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