We find explicit analytical formulae for the time dependence of the probability of the number of Okazaki fragments produced during the process of DNA replication. This extends a result of Cowan on the asymptotic probability distribution of these fragments.

During DNA replication, small fragments of DNA are formed. These have been observed experimentally and the mechanism of their formation modelled mathematically. Using the stochastic model of Cowan and Chiu (1992), (1994), we find the probability distribution of the number of fragments. A new discrete distribution arises. The work has interest as an application of the recent theory on quasirenewal equations in Piau (2000).

The double-stranded molecule, DNA, has the unique property of replication and, because of this, it is the central molecule of life. The mechanism of replication for each single strand is intricate, involving enzymes which move along each of the single strands building a complementary copy. At the frontier of this action, the events have a strong stochastic character due to the random location on the DNA of key ‘sites' where copying commences. A model of this process is analysed. The central problem of interest is the mean length of certain ‘islands' of newly replicated DNA developed at the randomly located ‘sites'. These islands, which have been observed experimentally, are called Okazaki fragments.