The Tail of the Convolution of Densities and its Application to a Model of HIV-Latency Time

Abstract

Let $p(x)$ and $q(x)$ be density functions and let $(p \ast q)(x)$ be their convolution. Define $w(x) = -(d/dx)\log q(x) \text{and} v(x) = -(d/dx)\log p(x).$ Under the hypothesis of the regular oscillation of the functions $w$ and $v$, the asymptotic form of $(p \ast q)(x)$, for $x \rightarrow \infty$, is obtained. The results are applied to a model previously introduced by the author for the estimation of the distribution of HIV latency time.