REAL

Limit theorems on the direct product of a non-compact Lie group and a compact group

Major, Péter and Pap, Gyula (2005) Limit theorems on the direct product of a non-compact Lie group and a compact group. Studia Scientiarum Mathematicarum Hungarica, 38 (1). pp. 279-297. ISSN 0081-6906

[img] Text
1120585.pdf
Restricted to Registered users only

Download (175kB) | Request a copy

Abstract

Let us consider a triangular array of random vectors (X-j((n)) , Y-j((n))), n = 1,2,..., 1 less than or equal to j less than or equal to k(n), such that the first coordinates X-j((n)) take their values in a non-compact Lie group and the second coordinates Y-j((n)) in a compact group. Let the random vectors (X-j((n)) , Y-j((n))) be independent for fixed n, but we do not assume any (independence type) condition about the relation between the components of these vectors. We show under Icn kn fairly general conditions that if both random products S-n = Pi (kn)(j=1) X-j((n)) and Tn = Pi (kn)(j=1) Y-j((n)) have a limit distribution, then also the random vectors (S-n,T-n) converge in distribution as n --> infinity. Moreover, the non-compact and compact coordinates of a random vector with this limit distribution are independent.

Item Type: Article
Subjects: Q Science / természettudomány > QA Mathematics / matematika
Depositing User: Erika Bilicsi
Date Deposited: 09 Apr 2013 11:38
Last Modified: 09 Apr 2013 11:38
URI: http://real.mtak.hu/id/eprint/4688

Actions (login required)

Edit Item Edit Item