Power time change of a Bessel process
= Power time change of a Bessel process
{c}
If $X$ is a Bessel process of dimension $d$ and $\alpha>0$, then $X^\alpha$, after the clock $\alpha^2\int X_s^{2\alpha-2}ds$, is a Bessel process of dimension
$$
d'=2+\frac{d-2}{\alpha}.
$$