The variance process in the Heston model satisfy a CIR process: [d V_{t}=kappaleft(bar{V}-V_{t} ight)+sigma sqrt{V_{t}} d W_{t}]

The variance process in the Heston model satisfy a CIR process:

\[d V_{t}=\kappa\left(\bar{V}-V_{t}\right)+\sigma \sqrt{V_{t}} d W_{t}\]

Use Ito to calculate the dynamics of the volatility process \(U_{t}=\sqrt{V_{t}}\). Under which conditions on the parameters \(\kappa, \bar{V}\), and \(\sigma\) the process becomes an Ørnstein-Uhlenbeck process, i.e. of the form

\[d U_{t}=\gamma X_{t} d t+\delta d W_{t}\]

for some parameters \(\delta\) and \(\gamma\) ?