Shot noise systems with random relaxations.

We explore a model of a random relaxation shot noise system in which (i) the shot inflow is a general Poisson point process, with possibly infinite Poissonian rates; and (ii) the exponential relaxations governing the shot decay are randomized. This system model is applicable to physical environments polluted by radioactive contamination of heterogeneous types. The statistics of random relaxation shot noise systems are analyzed quantitatively and comprehensively: stationary structure, correlation structure, process distribution, fractality and asymptotic fractality, and the display--both separately and simultaneously--of the Noah and Joseph effects. Results are obtained explicitly and in closed form, and facilitate the design of tractable shot noise systems with unique features.