The space- and energy-dependent theory of reactor-noise analysis has been developed using Langevin's technique starting from the transport equations. The theory includes delayed neutrons. The correlation function and the power spectral density for the detection rate, as well as for the neutron density, have been obtained. The application of the general theory to simple reactor models has been discussed and illustrated by considering the one-speed transport and one-speed diffusion approximations. The connection between Langevin's technique and the doublet theory based on the Liouville equation has been established. It has been found that both formulations yield identical results and that the postulates of Langevin's technique are justified for the study of neutron distributions.