ABSTRACT

This paper concerns the Stepanov-like pseudo almost periodicity in distribution for a stochastic process and optimal control. Using the analytic semigroup theory, fractional power operators, stochastic analysis theory and fixed point strategy, we obtain the existence of Stepanov-like pseudo almost periodic in distribution mild solutions for impulsive partial stochastic functional differential equations under non-Lipschitz conditions. The existence of optimal pairs of system governed by impulsive partial stochastic control systems is also presented. Finally, an example is given for demonstration.

中文翻译：

---

类Stepanov型伪几乎周期分布和脉冲偏随机微分方程的最优控制

抽象的

本文涉及随机过程中的Stepanov型伪几乎周期性分布和最优控制。使用解析半群理论，分数次幂算子，随机分析理论和不动点策略，我们获得了非Lipschitz条件下脉冲局部随机泛函微分方程在分配温和解中存在Stepanov型伪几乎周期性的情况。还提出了由脉冲部分随机控制系统控制的最优系统对的存在。最后，给出一个示例进行演示。