The Stability Of Expectation Programming

The stability of the optimal values and the optimal solutions set on random variable of expectation programming is discussed in this paper.The paper contains two chapters.Chapter 1 is the preliminaries. In probability, we simply introduce some basic concepts and lemmas about real-valued random variables and distribution functions, especially, the important and basic properties about characteristic functions are introduced. At last, the semi-continuity, closure, compactness of set-valued maps are introduced in the set-valued analysis.Chapter 2 is the main content of this paper. At first, we make the space of distribution functions of random variables a distance space after enduing it a proper distance, then making it a complete distance space. What is said above is the difficult part of this paper. At the same time, it is the feature of the paper. After getting some properties about expectation programming, we study the stability of the optimal values and the optimal solutions set of expectation programming with the tool of set-valued mappings, and some results of stability are obtained.