A QUADRATIC REGRESSION PROBLEM FOR TWO-STATE ALGEBRAS WITH AN APPLICATION TO THE CENTRAL LIMIT THEOREM-Reference-Cited by-同舟云学术

A QUADRATIC REGRESSION PROBLEM FOR TWO-STATE ALGEBRAS WITH AN APPLICATION TO THE CENTRAL LIMIT THEOREM

Published:2009-06 Issue:02 Volume:12 Page:231-249
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:

BOŻEJKO MAREK¹,BRYC WŁODZIMIERZ²

Affiliation:

1. Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

2. Department of Mathematical Sciences, University of Cincinnati, PO Box 210025, Cincinnati, OH 45221–0025, USA

Abstract

We extend the free version8 of the Laha–Lukacs theorem to probability spaces with two states. We then use this result to generalize the noncommutative central limit theorem of Kargin23 to the two-state setting.

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/S0219025709003616

Reference33 articles.

1. Notions of Independence Related to the Free Group

2. L. Accardi, Y. Hashimoto and N. Obata, Quantum Probability (Gdańsk, 1997), Banach Center Publ. 43 (Polish Acad. Sci., 1998) pp. 9–24.

3. Free martingale polynomials

4. Appell polynomials and their relatives II. Boolean theory

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A construction which relates c-freeness to infinitesimal freeness;Advances in Applied Mathematics;2019-09

2. New characterization of two-state normal distribution;Infinite Dimensional Analysis, Quantum Probability and Related Topics;2014-08-05

3. Semigroups of Distributions with Linear Jacobi Parameters;Journal of Theoretical Probability;2012-02-10

4. Limit Theorems for Additive Conditionally Free Convolution;Canadian Journal of Mathematics;2011-02-01

5. Two-state free Brownian motions;Journal of Functional Analysis;2011-01