Poisson point processes with detection and rest

Using the Poisson point process we model how the SiPM works and derive the non-linear response formula of the SiPM. Using this non-linear response formula we are able to capture the mean and variance saturation phenomena near the infinity and the linear behavior of the mean and variance near 0.We also introduce a different model of the SiPM. Under this different model we show the mean and variance saturation phenomena near the infinity and the linear behavior of the mean and variance near 0. We provide some open problems on this different model.