# Idea
The Ornstein-Uhlenbeck model is a [[leaky or unstable integrator|leaky integration]] model.
The basic [[drift diffusion model of choice and reaction time|drift diffusion model]] is the following:
$d x=A d t+c d W, \quad x_0=0$
The [[Ornstein-Uhlenbeck model]] extends the above to the following:
$d x=(\lambda x+A) d t+c d W, \quad x_0=0$
The rate of change of $x$ depends on its current value, with a magnitude controlled by the parameter $\lambda$, and $x$ can accelerate or decelerate toward a threshold/boundary depending on the sign of $\lambda$.
When $\lambda = 0$, the O-U model simplifies to the basic/pure [[drift diffusion model of choice and reaction time|DDM]].
# References
- [[Smith 2004 psychology and neurobiology of simple decisions]]
- [[Bogacz 2006 physics of optimal decision making]]
- [[Busemeyer 1993 decision field theory]]