Struct MilsteinScheme 

pub struct MilsteinScheme {
    pub drift: fn(f64) -> f64,
    pub diffusion: fn(f64) -> f64,
    pub diffusion_deriv: fn(f64) -> f64,
}

Milstein scheme for SDEs: dX_t = μ(X_t) dt + σ(X_t) dW_t.

The Milstein correction adds a term ½ σ σ’ ((ΔW)² - Δt) to achieve strong order 1.0 convergence (vs. Euler-Maruyama’s order 0.5).

Fields

drift: fn(f64) -> f64

Drift coefficient μ(x).

diffusion: fn(f64) -> f64

Diffusion coefficient σ(x).

diffusion_deriv: fn(f64) -> f64

Derivative of diffusion σ’(x).

Implementations

impl MilsteinScheme

pub fn new( drift: fn(f64) -> f64, diffusion: fn(f64) -> f64, diffusion_deriv: fn(f64) -> f64, ) -> Self

Create a new Milstein integrator.

pub fn simulate( &self, x0: f64, t_end: f64, n_steps: u32, seed: u64, ) -> Vec<(f64, f64)>

Simulate a path starting at x0 over [0, t_end] with n_steps steps.

Returns (time, X_t) pairs.

pub fn monte_carlo_mean( &self, x0: f64, t_end: f64, n_steps: u32, n_paths: u32, seed: u64, ) -> f64

Estimate the mean E[X_T] using Monte Carlo with n_paths paths.