Abstract
Abstract. An ecient method for the exact numerical
simulation of semi-Markov processes is used to study
minimal models of the control of eye movements in
reading. When we read a text, typical sequences of
®xations form a rather complicated trajectory ± almost
like a random walk. Mathematical models of eye
movement control can account for this behavior using
stochastic transition rules between few discrete internal
states, which represent combinations of certain stages of
lexical access and saccade programs. We show that
experimentally observed ®xation durations can be
explained by residence-time-dependent transition prob-
abilities. Stochastic processes with this property are
known as semi-Markov processes. For our numerical
simulations we use the minimal process method (Gilles-
pie algorithm), which is an exact and ecient simulation
algorithm for this class of stochastic processes. Within
this mathematical framework, we study dierent forms
of coupling between eye movements and shifts of covert
attention in reading. Our model lends support to the
existence of autonomous saccades, i.e., the hypothesis
that initiations of saccades are not completely determined by lexical access processes.
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