Modern observations and models of various astrophysical objects suggest that many of their physical parameters fluctuate substantially at different spatial scales. The rich variety of the emission processes, including Transition Radiation but not limited to it, arising in such turbulent media constitutes the scope of Stochastic Theory of Radiation. We review general approaches applied in the stochastic theory of radiation and specific methods used to calculate the transition radiation produced by fast particles in the magnetized randomly inhomogeneous plasma. The importance of the theory of transition radiation for astrophysics is illustrated by one example of its detailed application to a solar radio burst, including specially designed algorithms of the spectral forward fitting.
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