= Brownian time reversal on a finite interval
{c}
{title2=$R_s=B_T-B_{T-s}$}
For standard <Brownian motion> and deterministic $T>0$, the process $R_s=B_T-B_{T-s}$, $0\leq s\leq T$, is standard <Brownian motion> on that interval in its own <natural filtration>. Disjoint reversed time intervals give independent centered normal increments with the correct variances. This is different from an arbitrary random-time shift, which can depend on future data. It is also different from the <time inversion of Brownian motion> transformation $tB_{1/t}$.
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