On the Law of Free Subordinators

Arizmendi, Octavio; Hasebe, Takahiro; Sakuma, Noriyoshi

ALEA : Latin American Journal of Probability and Mathematical Statistics, 2013, 10(1), 271-291

Permalink : https://hdl.handle.net/2115/75970

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ALEA Lat. Am. J. Probab. Math. Stat. 10-1_271-291	pdf	332 KB	286

アクセス権	open access
URI	https://hdl.handle.net/2115/75970
タイトル	On the Law of Free Subordinators
著者	Arizmendi, Octavio ; Hasebe, Takahiro ; Sakuma, Noriyoshi
著者名 Arizmendi, Octavio
e-Rad_Researcher 00633166 著者名 Hasebe, Takahiro
著者名 Sakuma, Noriyoshi
言語	英語
発行日	2013
収録物名	ALEA : Latin American Journal of Probability and Mathematical Statistics
巻(号)	10(1)
ページ	271-291
抄録	We study the freely infinitely divisible distributions that appear as the laws of free subordinators. This is the free analog of classically infinitely divisible distributions supported on [0,∞), called the free regular measures. We prove that the 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 weak convergence. In addition, we show that a symmetric distribution is freely infinitely divisible if and only if its square can be represented as the free multiplicative convolution of a free Poisson and a free regular measure. This gives two new explicit examples of distributions which are infinitely divisible with respect to both classical and free convolutions: χ2(1) and F(1, 1). Another consequence is that the free commutator operation preserves free infinite divisibility.
資源タイプ	学術雑誌論文
出版タイプ	Version of Record
PISSN	1980-0436