Loop-erasure of planar Brownian motion

The time reversal of a Brownian motion conditioned to exit at a boundary point can be coupled to radial ${\mathrm{SLE}}_2$ so that its loop-erasure is the radial curve. The coupling requires the Brownian path's first hit of each initial radial segment to occur at its tip. It is an existence theorem for a coupling and does not assert that the Brownian trace equals the simple radial curve, or that an elementary deterministic finite-loop algorithm is defined for all continuum paths.