A theory for determining the ratio of the prompt to the delayed neutronic response, Wp/Wd, of a self-powered vanadium detector using methods of stochastic processes are described. Experimental data are also presented. The technique makes use of the inherent reactor noise; it is based upon cross correlating the fluctuating detector current signals from the actual vanadium detector and from a (purely prompt responding) cobalt self-powered detector, both of which are located in a power reactor close to each other. Both the analysis in the time domain and in the frequency domain were used to extract the ratio Wp/Wd. The measurements were performed at the Halden Boiling Water Reactor at 7 MW(th) and the ratio Wp/Wd of a commercial vanadium detector has been determined to be (6.5 ± 0.35)%. The technique described offers several advantages over the commonly used transient measuring method.