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A Category of Probability Spaces
http://hdl.handle.net/2261/00079431
http://hdl.handle.net/2261/00079431203b1130-9cd7-40a4-a8d3-31ad548f8aa2
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jms260202.pdf (190.7 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2020-07-27 | |||||
| タイトル | ||||||
| タイトル | A Category of Probability Spaces | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | Conditional expectation | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | Radon-Nikodym derivative | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | category theory | |||||
| 資源タイプ | ||||||
| 資源 | http://purl.org/coar/resource_type/c_6501 | |||||
| タイプ | departmental bulletin paper | |||||
| 著者 |
Adachi, Takanori
× Adachi, Takanori× Ryu, Yoshihiro |
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| 著者所属 | ||||||
| 著者所属 | Graduate School of Management, Tokyo Metropolitan University | |||||
| 著者所属 | ||||||
| 著者所属 | Department of Mathematical Sciences, Ritsumeikan University | |||||
| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | We introduce a category $\Prob$ of probability spaces whose objects are all probability spaces and whose arrows correspond to measurable functions satisfying an absolutely continuous requirement. We can consider a $\Prob$-arrow as an evolving direction of information. We introduce a contravariant functor $\mathcal{E}$ from $\Prob$ to $\Set$, the category of sets. The functor $\mathcal{E}$ provides conditional expectations along arrows in $\Prob$, which are generalizations of the classical conditional expectations. For a $\Prob$-arrow $f^-$, we introduce two concepts $f^-$-measurability and $f^-$-independence and investigate their interaction with conditional expectations along $f^-$. We also show that the completion of probability spaces is naturally formulated as an endofunctor of $\Prob$. | |||||
| 書誌情報 |
Journal of Mathematical Sciences The University of Tokyo 巻 26, 号 2, p. 201-221, 発行日 2019-07-26 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 13405705 | |||||
| 書誌レコードID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AA11021653 | |||||
| Mathmatical Subject Classification | ||||||
| 60A99(MSC2010) | ||||||
| Mathmatical Subject Classification | ||||||
| 16B50(MSC2010) | ||||||
| Mathmatical Subject Classification | ||||||
| 60G20(MSC2010) | ||||||
| Mathmatical Subject Classification | ||||||
| 18B99(MSC2010) | ||||||
| 出版者 | ||||||
| 出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| 原稿受領日 | ||||||
| 2018-03-19 | ||||||
