xbeta
Ornstein-Uhlenbeck process

The Ornstein-Uhlenbeck process can be represented as a stochastic differential equation

dX(t)=θ(X(t)μ)dt+σdW(t)
d X(t) = -\theta(X(t) - \mu)\;dt + \sigma\;dW(t)

with r(0 )=r 0 and where W(t) is a Brownian motion. It is the continuous-time analog of a discrete AR(1) process.

References

Cox J. C., J. Ingersoll, and S. Ross (1985): ”A Theory of the Term Structure of Interest Rates” Econometrica 53, 385-407.