关于非负下半连续函数最优可测耦合的存在性及其应用

Existence and Application of Optimal Measurable Coupling with Respect to Non-Negative Lower Semi-Continuous Functions

本文证明了两个转移概率关于非负下半连续函数最优可测耦合的存在性定理．作为对这一结果的应用，推广了Ｓｔｒａｓｓｅｎ定理，进而证明了跳过程的随机可比性等价于保序耦合的存在性．

In this paper the existence theorem of the optimal measurable coupling of two transition probabilities on non-negative lower semi-continuous function is proved. As an application of this result, Strassen's theorem is generalized, moreover, it is proved that the existence of an order-preserving coupling of jump processes is equivalent to the stochastical comparability of jump processes.