## The Annals of Applied Probability

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

Simeon M. Berman

#### 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.

#### Article information

Source
Ann. Appl. Probab., Volume 2, Number 2 (1992), 481-502.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aoap/1177005712

Digital Object Identifier
doi:10.1214/aoap/1177005712

Mathematical Reviews number (MathSciNet)
MR1161063

Zentralblatt MATH identifier
0752.62014

JSTOR

Subjects
Primary: 60E99: None of the above, but in this section
Secondary: 60F05: Central limit and other weak theorems 92A15

#### Citation

Berman, Simeon M. The Tail of the Convolution of Densities and its Application to a Model of HIV-Latency Time. Ann. Appl. Probab. 2 (1992), no. 2, 481--502. doi:10.1214/aoap/1177005712. https://projecteuclid.org/euclid.aoap/1177005712