Brownian covariance kernel
= Brownian covariance kernel
{c}
The covariance kernel of standard <Brownian motion> on $[0,1]$ is $c(s,t)=\min(s,t)$. Its integral operator has eigenfunctions $\sqrt2\sin((k-\tfrac12)\pi t)$ and eigenvalues $((k-\tfrac12)\pi)^{-2}$.