  The number N of detectable (i.e. communicating) extraterrestrial
civilizations in the Milky Way galaxy is usually done by using the Drake
equation. This equation was established in 1961 by Frank Drake and was the
first step to quantifying the SETI field. Practically, this equation is rather
a simple algebraic expression and its simplistic nature leaves it open to
frequent re-expression An additional problem of the Drake equation is the
time-independence of its terms, which for example excludes the effects of the
physico-chemical history of the galaxy. Recently, it has been demonstrated that
the main shortcoming of the Drake equation is its lack of temporal structure,
i.e., it fails to take into account various evolutionary processes. In
particular, the Drake equation doesn't provides any error estimation about the
measured quantity. Here, we propose a first treatment of these evolutionary
aspects by constructing a simple stochastic process which will be able to
provide both a temporal structure to the Drake equation (i.e. introduce time in
the Drake formula in order to obtain something like N(t)) and a first standard
error measure.
