= Time reversal of a Brownian bridge
{title2=$(X_t)_{0\le t\le1}\overset{d}= (X_{1-t})_{0\le t\le1}$}
The <Brownian bridge covariance kernel> is invariant under reversing both times, and its mean is zero. The two centered <Gaussian processes> therefore have equal finite-dimensional laws. Equality on countably many rational coordinates transfers the event of continuity at zero to the reversed endpoint. Interior continuity then extends the rational-time limit to all times. This proves the terminal continuity of the <stochastic integral representation of a Brownian bridge>.
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