Existence and Application of Optimal Markovian Coupling with Respect to Non-Negative Lower Semi-Continuous Functions |
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Authors: | Shaoyi Zhang |
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Affiliation: | (1) Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China;(2) Department of Mathematics, Hubei Normal University, Huangshi 435002, P. R. China |
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Abstract: | 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) |
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Keywords: | Transition probability Markovian coupling Jump process |
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