Power-law shot noise and its relationship to α-stable processes

1/f^β-type spectral behavior has received considerable attention in the past few years because it arises from a wide range of nature phenomena. Several methods have been proposed for modeling a 1/f^β process. In this paper we consider a power-law shot noise model, and show that it gives rise to a power-law α-stable process if β < 1, or to a process with power-law α-stable increments if 1 < β < 3. Based on the relationship between α and β we propose a new method for the estimation of the spectral exponent of the sample spectrum, which is particularly robust in the case β < 1.