This paper deals with new stochastic modeling of very low tunneling currents in Non-Volatile Memories. For this purpose, we first develop current measurement method based on Floating Gate technique. In order to reach the long time behavior of electrical dynamic, we aim at using very basic tools (power supply, multimeter...) but still having a very good current resolution. Also, our measurement is led in a very particular low-noise environment (underground laboratory) allowing to keep the electrical contacts on the device under test as long as possible. After showing the feasibility of such measurements, we present a modeling approach of the charge loss process inside the Non-volatile Memories by using mathematical tool involving long memory effect. The model is based on stochastic counting process with memory effect yielding to a fractional relaxation equation for the charge loss over time. The main interest of the present model lies in the fact that the corresponding inversion problem involves only two parameters that can be carried out efficiently.