A stochastic model for eye movements during fixation on a stationary target

A stochastic model describing small eye movements occurring during steady fixation on a stationary target is presented. Based on eye movement data for steady gaze, the model has a hierarchical structure; the principal level represents the random motion of the image point within a local area of fixation while the higher level mimics the jump processes involved in transitions from one local area to another. Target image motion within a local area is described by a Langevin-like stochastic differential equation taking into consideration the microsaccadic jumps pictured as being due to point processes and the high frequency muscle tremor, represented as a white noise. The transform of the probability density function for local area motion is obtained, leading to explicit expressions for their means and moments. Evaluation of these moments based on the model are comparable with experimental results. A physiologically based criterion for the occurrence of local area changes is assumed and the renewal density of these transitions is obtained. These transitions are brought about by the occurrence of large saccades. Hence, our analysis leads us to derive expressions for the mean and moments of the occurrence of large saccades in a given time T. These predictions may be checked against experimental results.