Ornstein-Uhlenbeck Process

Parameters

Mean Level (μ): 0.0

Mean Reversion Speed (θ): 1.0

Volatility (σ): 0.5

dX = θ(μ - X)dt + σdW

Simulation

Number of Paths: 5

Time Steps: 500

Statistics

Sample Mean

Sample Variance

Theory Mean

Stationary Var

Autocorrelation

About

The Ornstein-Uhlenbeck process is a mean-reverting stochastic process. The parameter θ controls reversion speed, μ is the long-run mean, and σ is volatility. Used in interest rate models (Vasicek) and physics (velocity of Brownian particle).