= F-Brownian bridge
{c}
{title2=$\mathbb G_F(t)=\mathbb G(F(t))$}
For a <cumulative distribution function> $F$ and a standard <Brownian bridge> $\mathbb G$, the F-Brownian bridge is the centred <Gaussian process> $\mathbb G_F=\mathbb G\circ F$. Its <covariance> is $F(\min(s,t))-F(s)F(t)$, by substituting $F(s),F(t)$ into the bridge covariance. It can jump when $F$ jumps. Its law is tight in the <supremum norm>, since composition with $F$ is a continuous map from the separable space of continuous bridge paths.
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