Central Limit Theorem and convergence to stable laws in Mallows distance

Details Central Limit Theorem and convergence to stable laws in Mallows distance Central Limit Theorem and convergence to stable laws in Mallows distance

2004-06-10

arxiv.org/abs/math/0406218v2

Bernoulli vol 11, no. 5 (2005), 829\^A?"845

Mathematics

Probability

21 pages; improved version - one result strengthened, exposition improved, paper to appear in Bernoulli

Scientific paper

We give a new proof of the classical Central Limit Theorem, in the Mallows ($L^r$-Wasserstein) distance. Our proof is elementary in the sense that it does not require complex analysis, but rather makes use of a simple subadditive inequality related to this metric. The key is to analyse the case where equality holds. We provide some results concerning rates of convergence. We also consider convergence to stable distributions, and obtain a bound on the rate of such convergence.

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