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Fractal-Shot-Noise Driven Doubly Stochastic Poisson Point Process STEVEN B. LOWEN and MALVIN C. TEICH

We explore the behavior of the fractal-shot-noise driven doubly stochastic Poisson point process or FSNDP, for which the associated impulse response functions assume a decaying power-law form. For a variety of parameters of the process, we obtain expressions for the count number distribution and moments, Fano factor, normalized coincidence rate, power spectral density, and time probability densities. A number of these measures exhibit power-law dependencies, indicating fractal behavior. For certain parameters the power spectral density exhibits 1=f-type behavior over a substantial range of frequencies, so that the process serves as a 1=f point process for in the range 0 < < 2. We consider two physical processes that are well described by FSNDP: Cherenkov radiation from a random stream of charged particles, and di usion of randomly injected concentration packets.