This paper empirically tests a model of stochastic evolutions of prostate-specific antigen (PSA), a trigger for intervention in an early stage prostate cancer surveillance program. It conducts hypothesis testing of the Geometric Browning Motion model based on its attributes of independent increments and linearity of the variance in the increment length versus a wide range of stochastic and deterministic alternatives. These alternatives include the currently accepted deterministic growth model. The paper reports strong empirical evidence in favour of the Geometric Browning Motion model. A model that best describes PSA evolution is a prerequisite to the establishment of decision-making criteria for abandoning active surveillance (i.e. a strategy that involves close monitoring) in early stage prostate cancer. Thus, establishing empirically the type of PSA process is a first step toward the identification of more accurate triggers for abandoning active surveillance and starting treatment while the chances of curing the disease are still high. Copyright © 2011 John Wiley & Sons, Ltd.