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

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.

Actions (login required)

Edit Item