  The Neutron Transport Equation (NTE) describes the flux of neutrons through
inhomogeneous fissile medium. Whilst well treated in the nuclear physics
literature (cf. [9, 27]), the NTE has had a somewhat scattered treatment in
mathematical literature with a variety of different approaches (cf. [8, 25]).
Within a probabilistic framework it has somewhat undeservingly received little
attention in recent years; nonetheless, probabilistic treatments can be found
see for example [19, 26, 24, 29, 4, 3]. In this article our aim is threefold.
First we want to introduce a slightly more general setting for the NTE, which
gives a more complete picture of the different species of particle and
radioactive fluxes that are involved in fission. Second we consolidate the
classical c0-semigroup approach to solving the NTE with the method of
stochastic representation which involves expectation semigroups. Third we
provide the leading asymptotic of our multi-species NTE, which will turn out to
be crucial for further stochastic analysis of the NTE in forthcoming work [6,
5]. The methodology used in this paper harmonises the culture of expectation
semigroup analysis from the theory of stochastic processes against c0-semigroup
theory from functional analysis. In this respect, our presentation is thus part
review of existing theory and part presentation of new research results based
on generalisation of existing results.
