CHAPTER XIII - MARKOV CHAINS AND RADIATIVE TRANSFER

Abstract

This chapter discusses Markov chains and radiative transfer. A Markov chain is a steady-state Markov process, and a Markov process is a special stochastic process in which the object undergoing the process can remember at most one stage of the process back in time. The simpler the internal structure of an object undergoing a stochastic process, the more closely the process can be Markovian. Radiative transfer processes on discrete spaces can essentially be described by Markov chains—or, at most, Markov processes. The first and simplest of all connections that are established between radiative transfer and Markov chains are for the case of monochromatic radiative transfer on a discrete space where the radiance is governed by the scattering functions for elastic scattering. The transpectral scattering function is the concept within the continuous formulation of the theory that describes the details of heterochromatic radiative transfer, that is, the transfer of radiant energy from one frequency to another at a given point within a medium.