The work is an extended version of the report presented at the conference ICTT-26. In the Part I we derive the forward and backward time-dependent linear stochastic equations for probability density of the integer number of neutrons and delayed neutron precursors in distributed model of a nuclear reactor. In the Part II we derive the distributed criticality stochastic equations and obtain the analytical solutions for asymptotic neutron number probability density function for a reactor in a close-to-critical state.
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