Before revision: We study the left tail behavior of the logarithm of the distribution function of a sum of dependent positive random variables . Asymptotics are computed under the assumption that the marginal distribution functions decay slowly at zero, meaning that the their logarithms are slowly varying functions.
After revision: We study the left tail behavior of the distribution function of a sum of dependent positive random variables . Asymptotics are computed under the assumption that the marginal distribution functions decay slowly at zero, meaning that the their logarithms are slowly varying functions.