容度下的条件期望

Conditional Expectation under Capacity

本文研究了客度下的条件期望。首先,在凹容度下给出了条件期望的定义,得出其具有正时齐性、转移不变性、非对称性、次可加性和单调性;接着,证明了其仍然满足C,不等式、Jensen不等式、Hlder不等式和Minkowski不等式。

In this paper, we study about the conditional expectation under the capacity. Firstly, we introduce the concept of conditional Choquet expectation which is the conditional expectation with respect to concave capacity, and then we prove some properties of this concept, which include positive homogeneity, translation invariance, asymmetry, subadditivity and monotonicity. Then, we state that Cr inequality, Schwarz inequality, Holder＇ s inequality, Minkowski inequality and Jensen＇ s inequality still hold for this kind of conditional expectations.