构形空间上Rubinstein距离的上界及其应用
Upper bounds on Rubinstein distances on configuration spaces and applications
摘要：
本文给出了具有Poisson测度的位形空间上几种Rubinstein型距离的上界。我们的不等式涉及两个众所周知的梯度，在Malliavin演算的意义下，可以在这个空间上定义。实际上，我们表明，根据被认为是配置之间的距离，这是一个梯度或其他是最有效的。泊松和其他更复杂的过程之间的距离估计的一些应用程序也提供了，我们的结果尾部和等周估计的应用完成这项工作。
英文摘要：
In this paper, we provide upper bounds on several Rubinstein-type distances on the configuration space equipped with the Poisson measure. Our inequalities involve the two well-known gradients, in the sense of Malliavin calculus, which can be defined on this space. Actually, we show that depending on the distance between configurations which is considered, it is one gradient or the other which is the most effective. Some applications to distance estimates between Poisson and other more sophisticated processes are also provided, and an application of our results to tail and isoperimetric estimates completes this work.
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