Struct BrownianMotion 

pub struct BrownianMotion {
    pub dt: f64,
    pub sigma: f64,
    /* private fields */
}

Standard Wiener process (Brownian motion) W(t).

Generates paths where increments dW ~ N(0, dt). This is the foundation of most continuous-time stochastic models.

Fields

dt: f64

Time step for path simulation.

sigma: f64

Diffusion coefficient (sigma). Default is 1.0 for standard BM.

Implementations

impl BrownianMotion

pub fn new(dt: f64, seed: u64) -> Self

Creates a new standard Brownian motion with given time step and seed.

pub fn with_sigma(dt: f64, sigma: f64, seed: u64) -> Self

Creates a scaled Brownian motion with diffusion coefficient sigma.

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

Generate a path of n_steps from W(0) = 0.

Returns n_steps + 1 values (including initial W = 0).

pub fn variance_at(&self, t: f64) -> f64

Compute theoretical variance at time t = n_steps * dt.

For standard BM, Var[W(t)] = sigma^2 * t.

pub fn multi_path(&self, n_paths: usize, n_steps: usize) -> Vec<Vec<f64>>

Generate multiple paths for Monte Carlo. Returns matrix [path_idx][step].

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

Quadratic variation estimate for a path (should converge to sigma^2 * T).