A nonlinear filter with hysteresis is presented to detect binary signals. It is shown that key calculations for the bit error rate are reduced to the "exit problem" of stochastic differential equation theory. Employing this formalism, closed form expressions are derived in the transform domain for the probability density function of the filter output in the presence of additive white Gaussian noise. By taking inverse transformations, such expressions can be used to compute several performance measures of binary detectors with hysteresis nonlinearity. (C) 2001 Elsevier Science B.V. All rights reserved.