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OrnsteinUhlenbeck

oxiphysics_core::stochastic_processes

Struct OrnsteinUhlenbeck 

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pub struct OrnsteinUhlenbeck {
    pub theta: f64,
    pub mu: f64,
    pub sigma: f64,
    pub x0: f64,
    /* private fields */
}
Expand description

Ornstein-Uhlenbeck mean-reverting process.

SDE: dX = theta*(mu - X)dt + sigmadW

Uses exact discretisation: X(t+dt) = X(t)exp(-thetadt) + mu*(1-exp(-thetadt)) + sigmasqrt((1-exp(-2thetadt))/(2*theta)) * N(0,1)

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§theta: f64

Mean reversion speed (theta > 0).

§mu: f64

Long-run mean (mu).

§sigma: f64

Volatility (sigma).

§x0: f64

Initial value X(0).

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impl OrnsteinUhlenbeck

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pub fn new(theta: f64, mu: f64, sigma: f64, x0: f64, seed: u64) -> Self

Creates a new OU process.

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pub fn path(&self, t_end: f64, n_steps: usize) -> Vec<f64>

Exact simulation path using the conditional Gaussian formula.

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pub fn stationary_variance(&self) -> f64

Stationary variance: sigma^2 / (2*theta).

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pub fn autocorrelation(&self, tau: f64) -> f64

Autocorrelation at lag tau: exp(-theta * tau).

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