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

Vladimirov, Igor; Thompson, Bevan

doi:https://doi.org/10.1155/JAMSA/2006/42542

International Journal of Stochastic Analysis

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Volume 2006 | Article ID 042542 | https://doi.org/10.1155/JAMSA/2006/42542

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

Igor Vladimirov¹and Bevan Thompson¹

Received28 Dec 2004

Revised13 May 2005

Accepted13 May 2005

Published02 May 2006

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.

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Copyright

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.

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