Prove that the power of a Bessel process is another Bessel process time-changed: [qleft[R_{t}^{(u)} ight]^{1 / q}=R^{(u

Prove that the power of a Bessel process is another Bessel process time-changed:

\[q\left[R_{t}^{(u)}\right]^{1 / q}=R^{(u q)}\left(\int_{0}^{t} \frac{d s}{\left[R_{s}^{(u)}\right]^{2 / p}}\right)\]

where \(\frac{1}{p}+\frac{1}{q}=1, u>-\frac{1}{q}\).