Abstract
Let ( Y 1 , … , Y n ) have a joint n -dimensional Gaussian distribution with a general mean vector and a general covariance matrix, and let X i = e Y i , S n = X 1 + ⋯ + X n . The asymptotics of P ( S n > x ) as n → ∞ are shown to be the same as for the independent case with the same lognormal marginals. In particular, for identical marginals it holds that P ( S n > x ) ∼ n P ( X 1 > x ) no matter what the correlation structure is.
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