Brownian bridge independence from its endpoint
= Brownian bridge independence from its endpoint
{c}
For standard <Brownian motion>, the <Brownian bridge> $U_t=B_t-tB_1$, $0\leq t\leq1$, is independent of $B_1$. Every finite vector of bridge coordinates is jointly <multivariate normal> with $B_1$, and its cross-<covariances> with $B_1$ vanish. The <independence of uncorrelated jointly normal variables> and <independence extended from generating pi-systems> prove independence of the whole <stochastic process>.