= Solution
For the equation actually produced by the preceding construction, namely the <Bessel process> equation of dimension $2-1/\delta$, the drift has <Lipschitz continuity> on every compact subset of $(0,\infty)$. Starting at any positive time and position, <pathwise uniqueness> therefore makes the time-changed process agree until its first hit of zero with the <maximal local solution of a stochastic differential equation>. For $\delta>1$, its dimension lies in $(1,2)$, so it can hit zero; the time-change construction then supplies further excursions, whereas the maximal local solution on $(0,\infty)$ stops at that first hit.
For $\delta=1$, $X_s=|B_s|$ is <Reflected Brownian motion>; away from zero it agrees with the maximal local solution of $dX=d\widetilde B$. For the dimension-$\delta$ equation printed in the paper, the preceding construction does not agree with the maximal local solution unless $\delta=1$, for the coefficient mismatch established in part (d).
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