Analysis of a stochastic dynamical model of word-by-word sentence comprehension

An important class of computational cognitive models is based on stochasticdynamical systems. The SWIFT model of eye-movement control (Engbert,Longtin, & Kliegl, 2002) and the drift-diffusion model of perceptual decisionmaking (Ratcliff, 1978), for example, have driven progress in part because ofthe mathematical tools that the models afford researchers in analyzing experimentaldata and deriving new predictions. Stochastic dynamical models havealso been applied to word-by-word reading comprehension; however, theirinfluence has been limited so far by relatively ad hoc, analytically opaqueimplementations. Here, I describe a new model of incremental sentencecomprehension that models the parsing process as a series of continuous time,discrete-state random walks among potential syntactic analyses of thesentence so far. Reading can now be framed as a first-passage problem: howlong does it take arrive at a complete parse of the sentence so far, giventhe preceding words? This note describes in detail the derivation of variousstochastic quantities of interest, including predicted reading time distributionfunctions, and illustrates them with example simulations. The hope is thatthese analytical tools can drive new progress in the theory of word-by-wordreading comprehension.

On first passage times of sticky reflecting diffusion processes with double exponential jumps

We explore the first passage problem for sticky reflecting diffusion processes with double exponential jumps. The joint Laplace transform of the first passage time to an upper level and the corresponding overshoot is studied. In particular, explicit solutions are presented when the diffusion part is driven by a drifted Brownian motion and by an Ornstein–Uhlenbeck process.