Stochastic population processes in the theory of radiative transfer

Abstract

Summary Starting from a characterization of radiative transfer in terms of a collision rate λ and a single-collision transition probability Ψ, we study the distribution of the generalized state ζ(t) of a radiation particle at time t conditional on a specified initial state at time t = 0. The generalized state is a vector consisting of the state ω(t) at time t and the states ω 1, ω 2, …, ω n of the particle immediately after the collisions it experiences in the time interval (0, t]. The variable ζ(t) takes values in a population space and can be studied conveniently with the aid of a certain generating functional G. The first-collision integral equation and the backward integro-differential equation for G are derived. Simultaneous consideration of the first-collision and last-collision equations lead to a generalized reciprocity principle for G. First-passage problems are also considered. Finally a number of illustrative examples are given.