σ²/2θ (theory): —
Sample var: —
τ = 1/θ: —
About: The Ornstein-Uhlenbeck (OU) process is the continuous-time analogue of an AR(1) process: dX = −θX dt + σ dW, where θ > 0 is the mean-reversion rate and σ is noise amplitude. It is the unique stationary Gaussian-Markov process. The stationary distribution is N(0, σ²/2θ) and autocorrelation decays as e^{−θτ}, giving correlation time 1/θ. The OU process models interest rates (Vasicek model), particle velocities in Brownian motion (Langevin equation), and neuronal membrane potentials.