Struct BrownianMotion 

pub struct BrownianMotion {
    pub x_0: f64,
    pub drift: f64,
    pub volatility: f64,
    /* private fields */
}

Standard Brownian motion dX = μ dt + σ dW, X(0) = x₀. Useful as a baseline simulator for testing the trait plumbing and as a building block for composite SDEs. Defaults: x₀ = 0, μ = 0, σ = 1.

Papers

• Brown, R. (1828) — A Brief Account of Microscopical Observations. The phenomenon.
• Wiener, N. (1923) — Differential Space, Journal of Mathematics and Physics 2: 131–174. The mathematical construction.
• Itô, K. (1944) — Stochastic Integral, Proceedings of the Imperial Academy 20(8): 519–524. Itô calculus underpinning every SDE in this crate.

Fields

x_0: f64

drift: f64

volatility: f64

Implementations

impl BrownianMotion

pub fn new(seed: u64) -> Self

pub fn with_drift(self, mu: f64) -> Self

pub fn with_volatility(self, sigma: f64) -> Self

pub fn with_initial(self, x_0: f64) -> Self

Trait Implementations

impl SimulationModel for BrownianMotion

type State = f64

Per-path state snapshot. Required to be Clone so the MC loop can keep a working copy per path while also capturing snapshots at each observation date. Small scalar states (HW, BM, GBM) stay Copy-derived and pay no runtime cost; variable-size states (the generalised FMM, which carries Vec<f64> per-rate buffers) satisfy Clone with a single heap copy per captured observation.

fn initial_state(&self) -> Self::State

State at the valuation date (t = 0).

fn step(&mut self, state: &Self::State, _t: f64, dt: f64) -> Self::State

Advance state by dt starting at year-fraction t. The implementation may consume draws from the model’s internal RNG.