#### Technical Report USC-SIPI-237

“Sums of Independent, Symmetric Stable Random Variables of Different Characteristic Exponents: Study of their Distribution and Application to Stochastic Transient Detection”

by George A. Tsihrintzis and Chrysostomos L. Nikias

July 1993

We study the structure of the probability density function of random variables which are formed as the sum of two or more independent, symmetric stable random variables of different characteristic exponents. We present two asymptotic series expansions, valid for small and for large arguments, respectively. As an application of the theory, we develop a receiver which detects impulsive stochastic transients superimposed on Gaussian background noise and show that the new detector outperforms square-- and _th --law detectors.

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