On Neutron Branching Processes

A statistical theory of the neutron transport process has been discussed by Harris [[I] and Mullikin Q7J. They considered the neutron population by generation rather than in real time and formulate them as a discretetime branching process. In this paper, we will formulate the neutron transport process as a continuous time branching process and study asymptotic properties of the neutron population. As a fundamental equation, we have a non-linear equation like (1.3) and our results may be regarded, as a problem in analysis, to be concerned with the asymptotic properties of solutions of such a non-linear equation. In such study, a linearized Boltzman equation, which is the dual of the evolution equation for expectation semigroup, plays important role. In this paper, we are mainly concerned with a monoenergetic and isotropic transport process on bounded domain in R, though a more general case can be treated by the same method. Also, our method can be applied to a general class of branching processes including branching diffusion processes but we will not go further into such generalizations.