Use It's lemma to express (d F) given that (F(x)=x^{1 / 2}), where the stochastic process (left{S_{t},

Use Itô's lemma to express \(d F\) given that \(F(x)=x^{1 / 2}\), where the stochastic process \(\left\{S_{t}, t \geq 0\right\}\) satisfies the stochastic differential equation

\[d S_{t}=\alpha\left(\beta-S_{t}\right) d t+\sigma \sqrt{S_{t}} d Z_{t}\]

where \(\alpha, \beta\) and \(\sigma\) are positive constants and \(\left\{Z_{t}, t \geq 0\right\}\) a standard Brownian motion.