A simplified stochastic model based on the forward stochastic model in the stochastic kinetics theory and the Itô stochastic differential equations is newly developed for treating monoenergetic space-time nuclear reactor kinetics in one dimension. The stochastic space-dependent kinetics model (SSKM) is tested against the Monte Carlo calculations for cases of uniform slab reactors with one delayed-neutron precursor group. The results show that the SSKM is in good agreement with the Monte Carlo method and can be used to describe the actual random space-time-dependent behavior of a nuclear reactor. Moreover, the SSKM can generalize the stochastic point-kinetics model.

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