Convergence to Stable Laws in the Space D
نویسندگان
چکیده
منابع مشابه
On the rate of convergence to bivariate stable laws
In the paper a distribution function of a sum of independent non-identically distributed bivariate random vectors is approximated by distribution function of a stable vector and the accuracy of such approximation is estimated. The obtained general result is only a little bit worse when compared with known estimates for the case of multivariate independent and identically distributed random vect...
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It is known that in the case of convergence to a normal law, the uniform rate of convergence is completely determined by the rate of convergence at points near the origin, up to terms of order n~; see [6, pp. 12, 46]. In this paper we show that results of this nature hold true for convergence to non-normal stable laws, provided the centering point is taken as the mode of the limit distribution....
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Central Limit Theorem and convergence to stable laws in Mallows distance
We give a new proof of the classical Central Limit Theorem, in the Mallows (Lr-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 converge...
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ژورنال
عنوان ژورنال: Journal of Applied Probability
سال: 2015
ISSN: 0021-9002,1475-6072
DOI: 10.1017/s002190020001216x