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Stochastic population processes in the theory of radiative transfer

Published online by Cambridge University Press:  14 July 2016

P. J. Brockwell
P. J. Brockwell*
Affiliation:
Michigan State University
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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 ω1, ω2, …, ωn 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.

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 2 , August 1970 , pp. 272 - 290
Copyright
Copyright © Applied Probability Trust 1970 

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