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