An Analogue of the LÉvy-CramÉr Theorem for Multi-Dimensional Rayleigh Distributions

preprint2010arXivOpen access

Abstract

In the present paper we prove that every k-dimensional Cartesian product of Kingman convolutions can be embedded into a k-dimensional symmetric convolution (k=1, 2, ...) and obtain an analogue of the Cramér-Lévy theorem for multi-dimensional Rayleigh distributions.

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