Modeling elaborate dead time in reactor monitoring using SDE's

Dead time loses, caused due to a short time period following a detection in which the detection system is not operational, is perhaps the most prominent effect in non-ideal detector behavior. The dead time effect has a very strong and noticeable effect on reactor monitoring and physical in-pile experiments. The dead time effects has been largely studied in the past, by numerous authors. In the most basic setting, assuming that the the dead time is fixed and that the count distribution is strict Poissonic, the proper corrections for the count losses are well known for many years. However, a full quantification of the dead time loses in more elaborated settings, such as non-constants dead time or when the waiting time between consecutive detections is not exponential (such as in highly multiplicative systems) are still a subject of interest, and are not fully understood. In the present study we introduce a stochastic model, using Ito Stochastic Differential Equation, for the detector response with a random dead time (both paralyzing and non-paralyzing) in a sub-critical reactor under the point model approximation. Some specific new results are tested against experimental and simulation results, showing full agreement with the theoretical predictions.