Radiance uses a non-deterministic (stochastic), light-backwards ray tracing algorithm to solve the lighting for a given simulation. This involves sending, or tracing, thousands to many millions of rays into the scene, looking for light. The more rays you send, the closer to reality[TM] the result. But even millions of rays will never equal the billions of photons bouncing around in the real scene. It's only the sheer number of photons that gives a physical scene the appearance of stability. In a simulation, we're sampling mathematical models of light and materials, and light is "wiggly", so in our approximations, yes, we will likely get small variations from one simulation to the next. The further from the light source the sample point is (more indirect bounces), the more important it becomes to sample aggressively to at least get close to a stable result as well.

In short, if you are seeing wildly different results from one run to the next (of the same scene), you need to increase the simulation parameters (i.e. send more rays). Radiance is wildly configurable in this area and the process of tuning the simulation parameters to achieve an accurate result in a reasonable timeframe is equal parts art and science.