@article{a04bb450dc2911df825b000ea68e967b,
title = "On the density of the sum of two independent Student t-random vectors",
abstract = "In this paper, we find an expression for the density of the sum of two independent d-dimensional Student t-random vectors X and Y with arbitrary degrees of freedom. As a byproduct we also obtain an expression for the density of the sum N+X, where N is normal and X is an independent Student t-vector. In both cases the density is given as an infinite series, where fn is a sequence of probability densities on Rd and (cn) is a sequence of positive numbers of sum 1, i.e. the distribution of a non-negative integer-valued random variable C, which turns out to be infinitely divisible for d = 1 and d = 2. When d = 1 and the degrees of freedom of the Student variables are equal, we recover an old result of Ruben.",
keywords = "Faculty of Science, sandsynlighedsregning, Student t-fordelinger, Student t-distribution, convolution, infinite divisibility",
author = "Christian Berg and Christophe Vignat",
year = "2010",
month = jul,
doi = "10.1016/j.spl.2010.02.019",
language = "English",
volume = "80",
pages = "1043--1055",
journal = "Statistics & Probability Letters",
issn = "0167-7152",
publisher = "Elsevier BV * North-Holland",
}