MONOTONIC INDEPENDENCE, MONOTONIC CENTRAL LIMIT THEOREM AND MONOTONIC LAW OF SMALL NUMBERS-Reference-Cited by-同舟云学术

MONOTONIC INDEPENDENCE, MONOTONIC CENTRAL LIMIT THEOREM AND MONOTONIC LAW OF SMALL NUMBERS

Published:2001-03 Issue:01 Volume:04 Page:39-58
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

MURAKI NAOFUMI¹

Affiliation:

1. Mathematics Laboratory, Iwate Prefectural University, Takizawa, Iwate 020-0193, Japan

Abstract

A notion of "monotonic independence" is formulated in the setting of C*-probability space. Based on this independence, a noncommutative central limit theorem and a noncommutative law of small numbers are given.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025701000334

Reference12 articles.

1. Interacting Fock Spaces and Gaussianization of Probability Measures

2. Notions of Independence Related to the Free Group

3. Convolution and limit theorems for conditionally free random variables

4. An example of a generalized Brownian motion

5. New Examples of Convolutions and Non-Commutative Central Limit Theorems

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