The Ornstein–Uhlenbeck process links a Brownian particle's velocity under friction to finance's Vasicek interest-rate model

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The sourcing here is Tier 4 (Wikipedia), acceptable for settled definitional and uncontested historical content but not as evidence of the underlying facts; the physics origin and the Vasicek application should be confirmed against the primaries.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.