The effect of a low level additive noise process on the input and output characteristics and threshold behavior of auditory nerves (ANs) is studied by means of a stochastic computational model. This paper derives the stochastic properties of the model input and output for adaptive threshold procedures. A closed form solution for the input, or amplitude, probability distribution is obtained via Markov models. The output statistics are derived by integrating over the noise-free probability mass function (PMF). All theoretical PMFs are verified by simulations. Theoretical threshold predictions as a function of noise level are made based on these PMFs and the results indicate that threshold is adversely affected by the presence of low levels of noise.