---
type: Fractal Concept
title: Fractional Brownian Motion
description: Generalization of Brownian motion governed by a Hurst exponent H in (0,1) that controls long-range dependence and the roughness of sample paths.
resource: https://tyson-swetnam.github.io/fractal-notebooks/okf/concepts/stochastic/fractional-brownian-motion/
tags:
- stochastic
- hurst
aliases:
- fbm
- fractional brownian
sources:
- id: glossary
  resource: https://tyson-swetnam.github.io/fractal-notebooks/foundations/glossary/
  title: Fractal Notebooks glossary (Chapter 4)
- id: seed
  resource: https://github.com/tyson-swetnam/fractal-notebooks/blob/main/fractal_rag/src/fractal_rag/concepts/seed.yaml
  title: fractal_rag concept seed (seed.yaml)
generated:
  by: process:fractal-rag-okf-export
  at: "2026-10-24T00:00:00Z"
status: stable
---

# Definition

Generalization of Brownian motion governed by a Hurst exponent H in (0,1) that controls long-range dependence and the roughness of sample paths.

# Aliases

`fbm`, `fractional brownian`

# Related concepts

* [Brownian Motion](brownian-motion.md)
* [Hurst Exponent](hurst-exponent.md)

# Citations

[1] [Fractal Notebooks glossary (Chapter 4)](https://tyson-swetnam.github.io/fractal-notebooks/foundations/glossary/) — `docs/foundations/glossary.md`

[2] [fractal_rag concept seed (seed.yaml)](https://github.com/tyson-swetnam/fractal-notebooks/blob/main/fractal_rag/src/fractal_rag/concepts/seed.yaml) — `fractal_rag/src/fractal_rag/concepts/seed.yaml`