---
title: "The Ornstein–Uhlenbeck process links a Brownian particle's velocity under friction to finance's Vasicek interest-rate model"
type: "claim"
status: "seedling"
source_url: "https://en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process"
source_title: "Ornstein%E2%80%93Uhlenbeck_process (Wikipedia)"
source_author: "Wikipedia — 'Ornstein–Uhlenbeck process'"
source_date: "2026-07-11T00:00:00.000Z"
source_quote: "The Ornstein–Uhlenbeck process is used in the Vasicek model of the interest rate."
source_tier: 4
audit_status: "flagged (Tier 4 Wikipedia; acceptable for the definitional/historical content per the sourcing floor, but the physics origin and the finance application should be confirmed against the primaries — Uhlenbeck & Ornstein, Phys. Rev. 36 (1930); Vasicek, J. Financial Economics (1977) — before load-bearing reuse. Verification routed to [[question-verify-ornstein-uhlenbeck-cross-domain-primaries]])"
provenance: "Promotion from 10-inbox/raw/2026-07-11-hop-stasis-is-an-ou-process.md, 2026-07-12"
origin: "batch"
derived_from: "10-inbox/raw/2026-07-11-hop-stasis-is-an-ou-process.md"
writer_model: "claude-opus-4-8"
date_created: "2026-07-12T00:00:00.000Z"
tags: ["ornstein-uhlenbeck","stochastic-processes","brownian-motion","quantitative-finance","vasicek-model","mean-reversion","cross-domain-bridge"]
---


The Ornstein–Uhlenbeck (OU) process is "named after Leonard Ornstein and George Eugene Uhlenbeck," and its "original application in physics was as a model for the velocity of a massive Brownian particle under the influence of friction" (Uhlenbeck & Ornstein, 1930). Where ordinary Brownian motion diffuses without bound, friction supplies a restoring force that pulls the velocity back toward zero — making the OU process a *mean-reverting* stochastic process with a stationary Gaussian distribution rather than an ever-spreading one.

That single mathematical feature — mean reversion toward a fixed level — is why the same equation reappears in quantitative finance: "The Ornstein–Uhlenbeck process is used in the Vasicek model of the interest rate," where interest rates are modeled as reverting toward a long-run mean rather than wandering freely. The physics object and the finance object are the same stochastic differential equation with the variables relabeled.

This note records the physics-to-finance leg of a broader cross-domain recurrence. The identical mean-reversion structure is what modern paleobiology fits to fossil stasis ([[claim-ou-model-recasts-stasis-as-active-mean-reversion-to-an-optimum]]) and what Mandt, Hoffman and Blei use to describe stochastic gradient descent near a loss minimum ([[claim-constant-sgd-near-a-loss-minimum-is-an-ornstein-uhlenbeck-process]]); the three legs are drawn together in [[observation-mean-reversion-to-an-optimum-recurs-across-fossil-stasis-bonds-and-sgd]].

The sourcing here is Tier 4 (Wikipedia), acceptable for settled definitional and uncontested historical content but not as evidence of the underlying facts; the physics origin and the Vasicek application should be confirmed against the primaries. See [[question-verify-ornstein-uhlenbeck-cross-domain-primaries]].