Mean-reversion has one number that matters: how fast does a deviation die. The half-life formula collapses continuous OU and discrete AR(1) onto the same one-liner.
Ornstein-Uhlenbeck is the simplest stochastic process that pulls back toward a long-run mean instead of drifting away. It is the gateway SDE for Vasicek and Hull-White short rates, the variance process inside Heston, and the spread inside every pairs trade. The single most useful applied fact about OU is the half-life of mean reversion — the time it takes for the expected deviation from the mean to drop by half — and it has the same closed form whether you write the model in continuous time or fit a discrete AR(1) regression.
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Worked example
Daily closing levels of a pairs-trading spread look stationary. You fit an AR(1) by OLS and find $r_{t+1} = 0.30 + 0.85\,r_t + \varepsilon_t$, with the implied long-run mean $\theta = 0.30 / (1 - 0.85) = 2.00$. How many trading days does it take for the expected deviation from $\theta$ to fall to half its starting value?
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Reflection
The half-life depends on $\kappa$ but not $\sigma$, while the stationary variance depends on $\sigma$ but only weakly on $\kappa$. Why do these two parameters separate so cleanly — what is each one actually controlling, and what would change if they were entangled?