期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2013
卷号：X
页码：271-291
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We study the freely infinitely divisible distributions that appear as thelaws of free subordinators. This is the free analog of classically infinitely divisibledistributions supported on [0,∞), called the free regular measures. We prove thatthe class of free regular measures is closed under the free multiplicative convolution,tth boolean power for 0 ≤ t ≤ 1, tth free multiplicative power for t ≥ 1 and weakconvergence. In addition, we show that a symmetric distribution is freely infinitelydivisible if and only if its square can be represented as the free multiplicative convolutionof a free Poisson and a free regular measure. This gives two new explicitexamples of distributions which are infinitely divisible with respect to both classicaland free convolutions: 2(1) and F(1, 1). Another consequence is that the freecommutator operation preserves free infinite divisibility.
