Implementation:Avhz RustQuant BrownianMotion

Knowledge Sources	RustQuant
Domains	Stochastic_Processes, Quantitative_Finance
Last Updated	2026-02-07 19:00 GMT

Overview

Concrete implementation of standard Brownian Motion (Wiener process) provided by the RustQuant library.

Description

Brownian Motion (also known as the Wiener process) is the fundamental continuous-time stochastic process defined by the SDE:

dX(t) = dW(t)

It has zero drift and unit diffusion. The process has independent, normally distributed increments with mean 0 and variance equal to the time increment. At any time t, X(t) ~ N(0, t) when starting from X(0) = 0.

This is a parameterless process -- no drift or volatility parameters are needed.

Usage

Use this process as the fundamental building block for more complex stochastic models. Standard Brownian Motion is used to generate random noise for simulating other SDEs, or directly when modeling phenomena with zero drift and unit variance rate.

Code Reference

Source Location

• Repository: RustQuant
• File: crates/RustQuant_stochastics/src/brownian_motion.rs
• Lines: 1-114

Signature

#[derive(Debug)]
pub struct BrownianMotion {}

impl BrownianMotion {
    pub fn new() -> Self
}

impl Default for BrownianMotion {
    fn default() -> Self
}

impl StochasticProcess for BrownianMotion {
    fn drift(&self, _x: f64, _t: f64) -> f64    // returns 0.0
    fn diffusion(&self, _x: f64, _t: f64) -> f64 // returns 1.0
    fn jump(&self, _x: f64, _t: f64) -> Option<f64>
    fn parameters(&self) -> Vec<f64>
}

Import

use RustQuant::stochastics::BrownianMotion;

I/O Contract

Inputs

Name	Type	Required	Description
(none)	--	--	No parameters required; constructed via BrownianMotion::new()

Outputs

Name	Type	Description
drift()	f64	Always returns 0.0
diffusion()	f64	Always returns 1.0
jump()	Option<f64>	Always returns None (no jump component)
parameters()	Vec<f64>	Returns an empty vector

Usage Examples

use RustQuant::stochastics::BrownianMotion;
use RustQuant::stochastics::{StochasticProcessConfig, StochasticScheme};

// Create a standard Brownian Motion
let bm = BrownianMotion::new();

// Configure simulation: x0=0.0, t_start=0.0, t_end=0.5, n_steps=100, 1000 paths
let config = StochasticProcessConfig::new(
    0.0, 0.0, 0.5, 100, StochasticScheme::EulerMaruyama, 1000, false, None
);

let output = bm.generate(&config);

// Access simulated paths
let paths = &output.paths;

Related Pages

• Principle:Avhz_RustQuant_Stochastic_Process_Simulation