A stochastic kinetic theory for space- and energy-dependent, zero power, nuclear reactor models is constructed from a last collision probability argument. The space and energy domains are partitioned into discrete cells. Equations are developed for the probabilities for transitions among the possible states of the reactor, and an equation is obtained for the probability generating function for these transition probabilities. Equations for the mean values, variances, covariances and correlation functions of the neutron and precursor distributions are derived. The stochastic distributions of neutrons and precursors are found to be space- and energy-dependent in subcritical reactors, but to attain a space- and energy- independent asymptotic form in supercritical reactors. The asymptotic distribution in a supercritical reactor is identical for the neutron and precursor distributions, and depends upon the manner in which the reactor is made supercritical. A method for applying the theory to low-source start-up calculations is suggested. The influence of spatial stochastic effects upon such calculations is demonstrated.