On the active periods of nonlinear Shot Noise

The statistical properties of the 'active' and 'silent' periods are analyzed, and the resulting 'on-and-off' Shot Noise structure is explored. Explicit formulae for means, variances, Laplace transforms, and other statistics are derived in closed-form. Based on this analysis, Shot Noise systems are categorized into three classes: transient, null-recurrent, and recurrent; and, these classes are characterized both analytically and probabilistically. Within the null-recurrent class, systems whose 'active periods' are governed by heavy-tailed probability distributions are further characterized.