A scalarization technique for computing the power and exponential moments of Gaussian random matrices (Q871347)

Summary: We consider the problems of computing the power and exponential moments \(EX^s\) and \(Ee^{tX}\) 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.