This paper focuses on optimal control of nonlinear stochastic delay system constructed through Teugels martingales associated with Lévy processes and standard Brownian motion, in which finite horizon is extended to infinite horizon. In order to describe the interacting many-body system, the expectation values of state processes are added to the concerned system. Further, sufficient and necessary conditions are established under convexity assumptions of the control domain. Finally, an example is given to demonstrate the application of the theory.

中文翻译：

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由Teugels Martingales控制的Lévy过程控制的非线性随机时滞系统的均值，无限视野，最优控制

本文重点研究了通过与Lévy过程和标准布朗运动关联的Teugels martingales构建的非线性随机时滞系统的最优控制，其中有限水平扩展到无限水平。为了描述相互作用的多体系统，将状态过程的期望值添加到相关系统中。此外，在控制域的凸度假设下建立了充分必要的条件。最后，通过实例说明了该理论的应用。