著者

村木 尚文

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:09172270)

巻号頁・発行日

vol.13, no.2, pp.137-149, 2003

参考文献数

37

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One of the main features of quantum probability(=noncommutative probability) is the diversity of notions of 'independence' for noncommutative random variables. Besides the three fundamental examples of universal independence (tensor, free and Boolean independence), there is another example called 'monotone independence' which was introduced and studied by the author. We give a brief review on 'monotone probability' which can be developed based on the notion of monotone independence. Especially we present the monotonic analogue of central limit theorem, law of small numbers, convolution, infinite divisibility and Levy-Hincin formula. Furthermore, we give a classification theorem for universal notions of independence.