Detection and adaptive estimation of stable processes with fractional lower-order moments

An important class of statistical models for nonGaussian phenomena is that of so-called heavy-tailed distributions, whose density functions decay in the tails less rapidly than the Gaussian density function. These distributions tend to produce large-amplitude excursions from the average value more frequently than the Gaussian distribution. Among all the heavy-tailed distributions, the family of stable distributions has been found to provide useful models for phenomena observed in many diverse fields, such as economics, physics and electrical engineering. It is capable of modeling a wide variety of nonGaussian phenomena, from those similar to the Gaussian to those similar to the Cauchy. This paper presents some preliminary results on signal detection and estimation under the nonGaussian stable assumption