Non-linear Shot Noise: Lévy, Noah, & Joseph

We introduce and study a generic non-linear Shot Noise system-model. Shots of random magnitudes arrive to the system stochastically, following an arbitrary time-homogeneous Poisson point process. After ‘hitting’ the system, the magnitude of an arriving shot decays to zero. The decay is governed by an arbitrary differential-equation dynamics. Shots are independent, and their overall effect on the system is additive: the system's noise level at time t equals the sum of the magnitudes, at time t, of all the shots arriving to the system prior to time t.