Before revision:   As a corollary , we characterize the limiting behavior of the conditional law of the Gaussian vector, given a linear combination of the exponentials of its components.
After revision:  These results can be used either to approximate the probability of tail events directly, or to construct variance reduction procedures to estimate these probabilities by Monte Carlo methods. In particular, we propose an efficient importance sampling estimator for the left tail of the distribution function of the sum of log-normal variables. As a corollary , we characterize the limiting behavior of the conditional law of the Gaussian vector, given a linear combination of the exponentials of its components.