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Joint cumulants for natural independence
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| Title: | Joint cumulants for natural independence |
| Authors: | Hasebe, Takahiro Browse this author →KAKEN DB | | Saigo, Hayato Browse this author |
| Keywords: | Natural independence | | cumulants | | non-commutative probability | | monotone independence |
| Issue Date: | 2011 |
| Journal Title: | Electronic Communications in Probability |
| Volume: | 16 |
| Start Page: | 491 |
| End Page: | 506 |
| Publisher DOI: | 10.1214/ECP.v16-1647 |
| Abstract: | Many kinds of independence have been defined in non-commutative probability theory. Natural
independence is an important class of independence; this class consists of five independences (tensor,
free, Boolean, monotone and anti-monotone ones). In the present paper, a unified treatment
of joint cumulants is introduced for natural independence. The way we define joint cumulants
enables us not only to find the monotone joint cumulants but also to give a new characterization
of joint cumulants for other kinds of natural independence, i.e., tensor, free and Boolean independences.
We also investigate relations between generating functions of moments and monotone
cumulants. We find a natural extension of the Muraki formula, which describes the sum of monotone
independent random variables, to the multivariate case. |
| Rights: | https://creativecommons.org/licenses/by/4.0/ |
| Type: | article |
| URI: | http://hdl.handle.net/2115/75998 |
| 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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