We review some basic concepts arising in the study of radiative transf
er in a stochastic atmosphere and consider their application to realis
tic atmospheric models. In particular, we examine the theory of Lindse
y and Jefferies which deals with multicomponent atmospheres whose stoc
hastic nature is entailed in the morphology of a network of boundaries
separating different atmospheric components. This theory is based on
the Markov assumption, that the probability, per unit path length alon
g a ray, for transition into another component is independent of the d
istance already traveled in the current component. We examine the appl
icability of the theory to models that are non-Markovian, paying parti
cular attention to the assignment of transition rates of such atmosphe
res. We consider in detail transition probabilities for spherical, tub
ular, conical, and other fluted structures, and show how the effects o
f overlap are to be incorporated for the case of a two-component atmos
phere. Comparisons of results obtained from the theory of Lindsey and
Jefferies with those found from Monte Carlo calculations, for models b
ased on identical structures randomly embedded into an ambient medium,
show that the Markov assumption promises to be a good approximation f
or the determination of the statistics of radiative transfer in a wide
variety of stochastic atmospheres, even when they are markedly non-Ma
rkovian.