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

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  • Igor Vladimirov
  • Bevan Thompson

Abstract

We consider the problems of computing the power and exponential moments E X s and E e t X of square Gaussian random matrices X = A + B W C 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.

Suggested Citation

  • Igor Vladimirov & Bevan Thompson, 2006. "A scalarization technique for computing the power and exponential moments of Gaussian random matrices," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-20, May.
    • Handle: RePEc:hin:jnijsa:042542
    DOI: 10.1155/JAMSA/2006/42542
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