On the Rate of Convergence in the CLT with Respect to the Kantorovich Metric
1994; Linguagem: Inglês
10.1007/978-1-4612-0253-0_12
AutoresSvetlozar T. Rachev, Ludger Rüschendorf,
Tópico(s)advanced mathematical theories
ResumoIn this paper, the rate of convergence in the CLT is estimated w.r.t. the Kantorovich metric for random variables with values in separable Banach spaces. In the first part, the rate in stable limit theorems for sums of i.i.d. random variables is considered. The method of proof is an extension of the Bergström convolution method. All assumptions regarding the domain of attraction are given in a metric form. In the second part of the paper an extension is given to the martingale case. For the proof we investigate smoothing properties of suitable conditional versions of the Kantorovich metric. As a consequence of the results for the Kantorovich metric one obtains rate of convergence results in stable limit theorems for martingales w.r.t. the Prohorov metric.
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