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Peer-reviewed Journal Articles, etc >
On the Law of Free Subordinators
| Title: | On the Law of Free Subordinators |
| Authors: | Arizmendi, Octavio Browse this author | | Hasebe, Takahiro Browse this author →KAKEN DB | | Sakuma, Noriyoshi Browse this author |
| Issue Date: | 2013 |
| Journal Title: | ALEA : Latin American Journal of Probability and Mathematical Statistics |
| Volume: | 10 |
| Issue: | 1 |
| Start Page: | 271 |
| End Page: | 291 |
| Abstract: | 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. |
| Type: | article |
| URI: | http://hdl.handle.net/2115/75970 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 長谷部 高広
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