We have developed a dynamic model of DNA replication control in bacterial cells and of the subsequent cell division. The main hypothesis is that a certain protein, which has a negative feedback regulation on its own production, is an essential factor in initiation of the replication. The model is stochastic in the sense that the kinetic association and dissociation processes are assumed to take place in accordance with a Poisson probability distribution with mean values that match experimentally determined constants. An important feature of our model is that it shows correlation between the magnitude of the kinetic rate constants and the size, stability and the dynamics of the cell. The model thus allows us to analyze the distribution of cell volumes at the time of initiation for different growth rate, different association and dissociation constants, and different promoter strengths.