Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 42542, 20 pages
A scalarization technique for computing the power and exponential
moments of Gaussian random matrices
Department of Mathematics, School of Physical Sciences, Faculty of Engineering, Physical Sciences, and Architecture, the University of Queensland, Brisbane 4072, QLD, Australia
Received 28 December 2004; Revised 13 May 2005; Accepted 13 May 2005
Copyright © 2006 Igor Vladimirov and Bevan Thompson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider the problems of computing the power and exponential
moments and of square Gaussian random
matrices for positive integer and real , where
is a standard normal random vector and , , are
appropriately dimensioned constant matrices. We solve the problems
by a matrix product scalarization technique and interpret the
solutions in system-theoretic terms. The results of the paper are
applicable to Bayesian prediction in multivariate autoregressive
time series and mean-reverting diffusion processes.