UNIVERSITY
OF WROCŁAW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
43.2 43.1 42.2 42.1 41.2 41.1 40.2
40.1 39.2 39.1 38.2 38.1 37.2 37.1
36.2 36.1 35.2 35.1 34.2 34.1 33.2
33.1 32.2 32.1 31.2 31.1 30.2 30.1
29.2 29.1 28.2 28.1 27.2 27.1 26.2
26.1 25.2 25.1 24.2 24.1 23.2 23.1
22.2 22.1 21.2 21.1 20.2 20.1 19.2
19.1 18.2 18.1 17.2 17.1 16.2 16.1
15 14.2 14.1 13.2 13.1 12.2 12.1
11.2 11.1 10.2 10.1 9.2 9.1 8
7.2 7.1 6.2 6.1 5.2 5.1 4.2
4.1 3.2 3.1 2.2 2.1 1.2 1.1
 
 
WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 33, Fasc. 2,
pages 243 - 254
 

RANDOM MATRICES BY MA MODELS AND COMPOUND FREE POISSON LAWS

Ayako Hasegawa
Noriyoshi Sakuma
Hiroaki Yoshida

Abstract: Recently, Pfaffel and Schlemm have investigated the Mar-chenko–Pastur type limit (n → ∞ and lim n∕p = λ > 0 n→ ∞ ) of the sample covariance matrix p-1X tX n n , where X n is the p ×n random matrix with dependence such that each row of X n is given by a certain linear process. They have also determined the limit spectral measure by giving the functional equation for its Stieltjes transform.

In this paper, we will see that such a limit spectral measure is a compound free Poisson law and, in the case where dependence is given by MA modeled Gaussian process, the sample covariance matrix can be regarded as compound Wishart matrix and, hence, gives the random matrix model for a compound free Poisson law. We will also give an application of compound Wishart matrix to the statistical data analysis of times series.

2000 AMS Mathematics Subject Classification: Primary: 46L54; Secondary: 60B20.

Keywords and phrases: Random matrix with dependent entries, asymptotic freeness, compound free Poisson laws, free Meixner laws.

Download:    Abstract    Full text   Abstract + References