Uniform approximation of the tail probability of weighted sums of subexponential random variables.

For subexponential random variablesXi, 1 ⩽i⩽n, the uniform asymptotic resultis established for 0 <an(x) ⩽ci⩽bn(x), 1 ⩽i⩽n, wherean(x) decreases to 0 andb(x) goes to infinity asxtends to infinity. It extends the current result when the subexponential random variablesXi’s are independent and gives the first uniform asymptotic result whenXi’s are dependent. [ABSTRACT FROM AUTHOR]