Full Counting Statistics of the Soft-Reset Process

A general formula for the cumulants of the soft- or emission-limited reset process of a floating storage node is derived from a hypoexponential-type probability distribution function (PDF) that models the process as a continuous-time Markov chain. Emission-number dependences of the cumulant expansion of the probability functions are compared with those of the steady shot noise process described by a Poissonian distribution. The cumulants of the soft reset (SR) nearly overlap with those of the Poissonian-type distribution in the early period of the emission process; at larger emission number, the SR deviates from the shot noise of the Poissonian process approaching an asymptote. This accounts for the leveling off in the SR.