Time dependent photon transport in a three dimensional interstellar cloud with stochastic clumps

We consider time dependent photon transport in a three dimensional interstellar cloud which occupies a three dimensional region V. One or more clumps of given shapes are present within V and their positions are determined by a suitable set of stochastic variables. If f is the photon number density in the cloud or in the clumps, then our mathematical model leads to two coupled initial value problems for the average photon density over the stochastic variables [f] and for f* = f - [f]. By using the theory of semigroups, we prove existence and uniqueness of a strongly continuous solution and examine the small fluctuation approximation of such a solution.