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

Vladimirov, I .G. and Thompson, H. B. (2006) A scalarization technique for computing the power and exponential moments of gaussian random matrices. Journal of Applied Mathematics and Stochastic Analysis, 2006 1-20. doi:10.1155/JAMSA/2006/42542


Author Vladimirov, I .G.
Thompson, H. B.
Title A scalarization technique for computing the power and exponential moments of gaussian random matrices
Journal name Journal of Applied Mathematics and Stochastic Analysis   Check publisher's open access policy
ISSN 1048-9533
1687-2177
Publication date 2006
DOI 10.1155/JAMSA/2006/42542
Volume 2006
Start page 1
End page 20
Total pages 20
Editor J Dshalalow (Editor-in-Chief)
Place of publication USA
Publisher Hindawi Publishing Corp.
Collection year 2006
Language eng
Subject C1
230203 Statistical Theory
780101 Mathematical sciences
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.
Formatted 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.
Q-Index Code C1
Additional Notes The paper provides a system-theoretic algorithm to exactly compute the moments of Gaussian random matrices arising in Bayesian forecasting of multivariate autoregressive time series and mean-reverting stochastic diffusion processes relevant to Econometrics and Adaptive Control. The statistical computing problem had previously been solved only approximately by Monte-Carlo simulations. H.B.Thompson was the CI of an ARC grant under which I.Vladimirov was employed.

 
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Created: Wed, 15 Aug 2007, 10:28:36 EST