---
title: "Do the primaries confirm the Ornstein–Uhlenbeck process's physics origin (Uhlenbeck & Ornstein 1930) and its use in the Vasicek interest-rate model?"
type: "question"
status: "open"
date_raised: "2026-07-12T00:00:00.000Z"
tags: ["ornstein-uhlenbeck","stochastic-processes","brownian-motion","quantitative-finance","vasicek-model","primary-source-verification"]
writer_model: "claude-opus-4-8"
---


Raised while promoting `10-inbox/raw/2026-07-11-hop-stasis-is-an-ou-process.md` into
[[claim-ornstein-uhlenbeck-process-links-brownian-motion-and-the-vasicek-model]]. That note rests
on Wikipedia (Tier 4) — acceptable for settled definitional/historical content per the sourcing
floor, but a pointer to the primaries, not evidence of them. The note stays `seedling` until read
against the source texts. Two documents, two verifications:

**1. Physics origin.** G. E. Uhlenbeck & L. S. Ornstein, "On the Theory of the Brownian Motion,"
*Physical Review* 36 (1930), 823–841. Confirm that the process introduced there is the
mean-reverting model of a massive Brownian particle's **velocity under friction** — i.e. that the
recorded gloss ("original application in physics was as a model for the velocity of a massive
Brownian particle under the influence of friction") is faithful to the paper, and that the
friction term is what supplies mean reversion.

**2. Finance application.** Oldřich Vašíček, "An equilibrium characterization of the term
structure," *Journal of Financial Economics* 5 (1977), 177–188. Confirm that the Vasicek short-rate
model is an Ornstein–Uhlenbeck process — a mean-reverting diffusion of the interest rate toward a
long-run level — i.e. that "the Ornstein–Uhlenbeck process is used in the Vasicek model of the
interest rate" is the same equation with variables relabeled, not a loose resemblance.

**Why it matters:** the physics-to-finance identity is the second leg of the cross-domain OU bridge
([[observation-mean-reversion-to-an-optimum-recurs-across-fossil-stasis-bonds-and-sgd]]). It is
uncontested textbook material, so priority is medium — but a cross-domain claim that a bridge note
leans on should sit on its primaries rather than on Wikipedia. Both papers are widely available
(Phys. Rev. archive; JFE / library routes).