Struct BrownianMotion 

pub struct BrownianMotion;

Parameters and generators for Brownian motion processes.

Implementations

impl BrownianMotion

pub fn standard(t: f64, n_steps: usize, seed: u64) -> Vec<f64>

Simulate a standard Brownian motion path W(t) on [0, T] with n_steps steps.

Returns a vector of length n_steps + 1 starting at 0, where increments are iid N(0, dt).

pub fn geometric( s0: f64, mu: f64, sigma: f64, t: f64, n_steps: usize, seed: u64, ) -> Vec<f64>

Simulate a Geometric Brownian Motion S(t) = S0 * exp((mu - 0.5*sigma^2)t + sigmaW(t)).

Returns the price path of length n_steps + 1.

pub fn fractional(hurst: f64, n_steps: usize, seed: u64) -> Vec<f64>

Simulate a Fractional Brownian Motion (fBm) path with Hurst exponent H.

Uses the Davies-Harte (spectral) method via a circulant embedding. Valid for H in (0, 1); H = 0.5 recovers standard BM.

pub fn quadratic_variation(path: &[f64]) -> f64

Compute the quadratic variation of a path (empirical check for BM).

For a standard BM of length T, the quadratic variation converges to T.

pub fn mean(path: &[f64]) -> f64

Compute the sample mean of a path.

pub fn variance(path: &[f64]) -> f64

Compute the sample variance of a path.