Transportation Distance and the Central Limit Theorem

Details Transportation Distance and the Central Limit Theorem Transportation Distance and the Central Limit Theorem

2006-07-04

arxiv.org/abs/math/0607089v1

Mathematics

Probability

Scientific paper

For probability measures on a complete separable metric space, we present sufficient conditions for the existence of a solution to the Kantorovich transportation problem. We also obtain sufficient conditions (which sometimes also become necessary) for the convergence, in transportation, of probability measures when the cost function is continuous, non-decreasing and depends on the distance. As an application, the CLT in the transportation distance is proved for independent and some dependent stationary sequences.

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