Simulation with fluctuating and singular rates

In this paper we present a method to generate independent samples for a general random variable, either continuous or discrete. The algorithm is an extension of the Acceptance-Rejectionmethod, and it is particularly useful for kinetic simulation in which the rates are fluctuating in time and have singular limits, as occurs for example in simulation of recombination interactions in a plasma. Although it depends on some additional requirements, the new method is easy to implement and rejects less samples than the Acceptance-Rejection method.