# Brownian Motion

Canonical: https://manyspace.aporia.systems/topics/brownian-motion-mth-stoch-340
Updated: 2026-10-13

Mathematics · Stochastic Processes · MTH-STOCH-340

- Difficulty: 4 / 5
- Importance: 5 / 5
- Study time: 6.5–12 h

construction, properties, non-differentiability, scaling

## Why it matters

Mathematics of random processes evolving over time; essential for finance, ML, statistical physics, communications and queuing.

## Where it is used

Options pricing, queue systems, recommendation algorithms, particle physics detection, noise in engineering systems.

## How you know you have learned it

Explain/derive key result from memory + solve 2 non-routine checks.

## What you need first

- [Sample Spaces & Events](https://manyspace.aporia.systems/topics/sample-spaces-events-mth-prob-196) (required)
- [Poisson Processes](https://manyspace.aporia.systems/topics/poisson-processes-mth-stoch-339) (required)
- [Sigma-Algebras & Measure Spaces](https://manyspace.aporia.systems/topics/sigma-algebras-measure-spaces-mth-meas-306) (helpful)

## What it opens

- [Stochastic Calculus Intro](https://manyspace.aporia.systems/topics/stochastic-calculus-intro-mth-stoch-342)

## Resources

- Probability and Random Processes (Grimmett & Stirzaker) — Grimmett & Stirzaker