= Integrated Brownian motion
{title2=$I_t=\int_0^tB_s\,ds$}
The ordinary time integral of standard <Brownian motion> is a centered <Gaussian process> with continuously differentiable paths and derivative $B_t$. For $0\leq s\leq t$, its <covariance> is $\mathbb E(I_sI_t)=s^2(3t-s)/6$, obtained by integrating the Brownian <covariance> $\min(u,v)$. Consequently $I_t$ has <normal distribution> $N(0,t^3/3)$. This time integral is distinct from the <Itô integral> with respect to <Brownian motion>.
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