带随机过程的随机规划问题──最优值过程与最优解集过程的鞅性

STOCHASTIC PROGRAMMING PROBLEM WITH RANDOM PROCESSES──THE MARTINGALE PROPERTIES OF ITS OPTIMAL VALUE PROCESS AND OPTIMAL SOLUTION SET PROCESSES

假设问题中所含随机过程为鞅，本文证明了带随机过程的随机规划问题其最优值过程与最化解集过程分别为实值上鞅与集值上鞅，且存在最优鞅解过程．

Under the assumption that the random process included in the problem is martingale, it is proved in this paper that the optimal value process and the optimal solution set processes are real-valued supermartingale and set-valued supermartingale respectively. Furthermore. there exists a optimal martingale solution process.