Approximations to sums of stationary and ergodic sequences by martingales are investigated. Necessary and sufficient conditions for such sums to be asymptotically normal conditionally given the past ...

This paper studies the approximation of extreme quantiles of random sums of heavy-tailed random variables, or, more specifically, subexponential random variables. A key application of this ...

An approximation for negative binomial sums involving a minimum of arithmetic is presented. Because of the relationship between negative binomial sums and regular binomial sums the approximation can ...