  We develop an approximate theoretical method to study discrete stochastic
birth and death models that include a delay time. We analyze the effect of the
delay in the fluctuations of the system and obtain that it can qualitatively
alter them. We also study the effect of distributed delay. We apply the method
to a protein-dynamics model that explicitly includes transcription and
translation delays. The theoretical model allows us to understand in a general
way the interplay between stochasticity and delay.
