A stochastic model of a reactor with a control rod is studied here. By assimilating populations of neutrons, of precursors and of absorbing atoms associated with control rod displacements to markovian random variables, the Chapman-Kolmogorov equation is established. Using Fokker-Planck and Langevin approximations, one obtains the noise spectral density P(f) of the control rod in terms of reactivity. Applied to a large bandwidth control system, commanded by a low efficient detector, the mode1 permits to obtain, from an experimental analysis of P(f), the value of αc = β/l where β is the total fraction of delayed neutrons and l, the average life time of neutrons.