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An important factor that may play a role in speech recognition by individuals with cochlear implants is that electrically stimulated nerves respond with a much higher level of synchrony than is normally observed in acoustically stimulated nerves. Recent work has indicated that the addition of noise to an electrical stimulus may result in neural responses whose statistical characteristics are more similar to those observed in acoustically driven neurons. Psychophysical data have indicated that performance on some tasks might also be enhanced by the addition of noise. However, little theoretical work has been done toward predicting the effect of noise on psychoacoustic measurements. In this paper, theoretical predictions of these effects are developed through the use of a stochastic computational model. The effect of additive noise on the input and output characteristics and aggregate threshold behavior of modeled auditory nerves (ANs) is specifically studied. This paper derives the stochastic properties of the model input and output when using adaptive threshold procedures. A closed form solution for the input, or amplitude, probability distribution is obtained via Markov models for both one-down one-up (1D1U) and two-down one-up (2D1U) experimental paradigms. The output statistics are derived by integrating over the noise-free probability mass function (PMF). All theoretical PMFs are verified by simulations with the model. Theoretical threshold is predicted as a function of noise level based on these PMFs and the predictions match simulated performance. The results indicate that threshold may be adversely affected by the presence of high levels of noise.