# Gaussian approximation of Gaussian scale mixture

For a given positive random variable V>0 and a given Z∼ N(0,1) independent of V, we compute the scalar t_0 such that the distance between Z√(V) and Z√(t_0), in the L^2() sense, is minimal. We also consider the same problem in several dimensions. Keywords: Normal approximation, Gaussian scale mixture, Plancherel theorem.

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