  Synchrotron emissivities, absorptivities, and Faraday rotation and conversion
coefficients are needed in modeling a variety of astrophysical sources,
including Event Horizon Telescope (EHT) sources. We develop a method for
estimating transfer coefficients that exploits their linear dependence on the
electron distribution function, decomposing the distribution function into a
sum of parts each of whose emissivity can be calculated easily. We refer to
this procedure as stochastic averaging and apply it in two contexts. First, we
use it to estimate the emissivity of an isotropic $\kappa$ distribution
function with a high energy cutoff. The resulting coefficients can be evaluated
efficiently enough to be used directly in ray-tracing calculations, and we
provide an example calculation. Second, we use stochastic averaging to assess
the effect of subgrid turbulence on the volume-averaged emissivity and along
the way provide a prescription for a turbulent emissivity. We find that for
parameters appropriate to EHT sources turbulence reduces the emissivity
slightly. In the infrared turbulence can dramatically increase the emissivity.
