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We define fractal shot noise, which is a stationary continuous-time process that is fundamentally different from fractional Brownian motion. Two applications in physics are considered: the mass distribution of collections of solid-particle aggregates and the electric field at the growing edge of a doped semiconductor quantum wire. For a broad range of parameters, the amplitude probability density function of this process is a L\'evy-stable random variable with dimension less than unity; it therefore does not converge to Gaussian form.
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Lowen et al. (1989) studied this question.
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