By using some quasi-renewal-like equations and functional differential equations, we explicitly compute the Laplace transforms of some random variables introduced by Cowan and Chiu in modeling the mechanism of replication of a DNA molecule [J. Appl. Probab. (1994) 31 301--308]. These Laplace transforms are expressed by means of infinite products arising in the theory of partitions.
"Some probability distributions in modeling DNA replication." Ann. Appl. Probab. 13 (3) 1207 - 1230, August 2003. https://doi.org/10.1214/aoap/1060202839