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Simulation of correlated normal random variables

Simulation of i.i.d. normal random variables is standard. Let us consider the Cholesky decomposition

$\displaystyle \Sigma = CC^t$ (47)

of the covariance matrix $ \Sigma$. If $ Z=(Z_i)_{i=1,\ldots,d+2}$ are $ d+2$ i.i.d. normal random variables, then

$\displaystyle (N_i)_{i=1,\ldots,d+2} = N = C\cdot Z$ (48)

contains $ d+2$ normally distributed random variables with covariances $ \Sigma$.

2003-10-24 Approximity