一类距离下的最优耦合

THE OPTIMAL MARKOVIAN COUPINGS FOR A SPECIFIC OF DISTANCE

研究了跳过程在一类距离ρ下的最优耦合，证明了在相当弱的条件下，如果存在保序耦合，则是ρ最优的，并且给出了ρ的明确表达式，还讨论了离散时间马氏链在该类距离下的最优耦合，结论与连续时间的情形是平等的。

The ρ-optimal couplings for a specific type of distance ρ are studied. It is proved that under the mild conditions, if there exists the order-preserving coupling O,then it is indeed one of the ρ-optimal couplings. The explicit representation of O is presented.Meanwhile, the optimal coupling of time-discrete Markov chains under this distance is discussed and the results obtained are parallel to these of time-continuous.