Shot noise displaying simultaneously the Noah and Joseph effects.

Shot noise processes displaying the Noah effect are of infinite variance. Hence the measurement of the correlation structure of such processes--indicating whether the Joseph effect is displayed as well--cannot be conducted via their autocovariance functions (which are undefined). To circumvent this problem, a Poisson-based analysis applicable to shot noise processes with infinite variance, as well as to shot noise processes with divergent noise levels, is developed. A Poissonian autocovariance function, which characterizes the process-distribution of general shot noise processes, is introduced. In particular, this function governs and quantifies the processes' stationary structure (amplitudal behavior) and correlation structure (temporal behavior). The "Poissonian methodology" developed enables a precise quantitative analysis of shot noise processes displaying simultaneously the Noah and Joseph effects.