带随机过程的随机规划问题最优解集的过程特性与稳定性

本文证明了带随机过程的随机规划问题最优解集做为集值随机过程的可测性、可测最优解选择过程的存在性。研究了最优解集过程的平稳性、马氏性以及最优值过程的鞅性和最优解集过程的集值鞅性。最后，讨论了在有限维分布意义下最优解集过程对所含随机过程参数的连续性以及最优值过程的稳定性。

PROCESS PROPERTIES AND STABILITY OF OPTIMAL SOLUTIONS AND VALUES OF STOCHASTIC PROGRAMMINGS WITH RANDOM PROCESSES

In this paper, the optimal solutions set of a stochastic programming problem is studied as a set-valued stochastic process, its measurability and existence of measurable selections are proved. The stationary property, Markoy Property and martingale property of the optimal solution sets process are discussed. The continuous dependence of the optimal solutions set process on the random process parameters and the stability of the optimal value process are also demonstrated.