- square root of step size—why? #followup - see [[Tuerlinckx 2001 a comparison of four methods for simulating diffusion process]] - see https://courses.washington.edu/matlab1/Lesson_18.html - [[diffusion model - sqrt(dt)]] - [[drift diffusion model of choice and reaction time]] # Idea Three properties of a diffusion process, for a given stimulus with strength $x$ (let accumulated evidence at time $t$ be $U(t)$): 1. At $t = 0$, the accumulated evidence is 0. 2. The momentary change in evidence is a random variable that is independent from moment to moment (i.e., it doesn't not change as a function of time). 3. The accumulated evidence $U(t)$ is normally distributed and has mean and variance: - $E[U(t)] = \mu t$ - $Var[U(t)] = \sigma^2t$ # References - [[Palmer 2005 the effect of stimulus strength]] - [Diffusion or random walk models of reaction time](https://courses.washington.edu/matlab1/Lesson_18.html)