Ornstein-Uhlenbeck Mean-Reverting Process Skill

Exact discrete transition simulation for stationary Gaussian mean-reverting stochastic processes.

flowchart TD
    State["Current Value x_t"] --> Drift["Reversion Drift: θ(μ - x_t)"]
    State --> Decay["Exact Exponential Transition Mean μ + (x - μ)e^{-θΔt}"]
    Decay --> Variance["Stationary Conditional Variance (σ^2 / 2θ)(1 - e^{-2θΔt})"]
    Variance --> Sample["Sample Gaussian Transition"]
    Sample --> Next["Updated Trajectory x_{t+1}"]

Features

• 100% Python Standard Library: Exact conditional distribution evaluation.
• Zero Discretization Bias: Avoids naive Euler approximations.
• Physical & Financial Applications: Models friction, velocity relaxation, and interest rates.