A comparison of four methods for simulating the diffusion process
Number of pages
SourceBehavior Research Methods, Instruments & Computers, 33, 4, (2001), pp. 443-456
Article / Letter to editor
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SW OZ DCC BI
Behavior Research Methods, Instruments & Computers
Four methods for the simulation of Wiener process with constant drift and variance are described. These four methods are : (1) approximating the diffusion process by a random walk with very small time steps; (2) drawing directly from the joint density of responses and reaction time by means of a (possibly) repeated application of a rejection algorithm; (3) using a discrete approximation to the stochastic differential equation describing the diffusion process and (4) a probability integral transform method approximating the inverse of the cumulative distribution function of the diffusion process. The four methods for simulating response probabilities and response times are compared on two criteria: simulation speed and accuracy of the simulation. It is concluded that the rejection-based and probability integral transform method perform best on both criteria, while the stochastic differential approximation is worst. An important drawback of the rejection method is that it is only applicable to the Wiener process while the probability integral transform method is more general.
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