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

Abstract In this paper, for two given transition probabilities, the existence of the optimal Markovian coupling with respect to a non-negative lower semi-continuous function is proved. As an application of this result, the well-known Strassen's theorem is generalized. Moreover, it is proved that the existence of an order-preserving Markovian coupling of two given jump processes is equivalent to their stochastical comparability. Research supported in part by DPFIHE (Grant No. 96002704) and NNSFC (Grant No. 19771008)