= Zero-start Ornstein-Uhlenbeck covariance
{title2=$\mathbb E[\sigma_t\sigma_s]=\frac{\kappa\tau}{2}(e^{-|t-s|/\tau}-e^{-(t+s)/\tau})$}
For $d\sigma=-\sigma\,dt/\tau+\sqrt\kappa\,dW$ with $\sigma_0=0$, the explicit <stochastic integral> is $\sigma_t=\sqrt\kappa\int_0^te^{-(t-u)/\tau}dW_u$. The <Itô isometry> on the overlap of the two integration intervals gives the displayed <covariance>. The second exponential records the zero initial condition; removing it gives the stationary <Ornstein-Uhlenbeck process> covariance.
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