Journal of Applied Mathematics and Stochastic Analysis 
Volume 2006 (2006), Article ID 42542, 20 pages
doi:10.1155/JAMSA/2006/42542

A scalarization technique for computing the power and exponential moments of Gaussian random matrices

Igor Vladimirov and Bevan Thompson

 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

Abstract

We consider the problems of computing the power and exponential moments EXs and EetX of square Gaussian random matrices X=A+BWC for positive integer s and real t, where W is a standard normal random vector and A, B, C 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.