Grateful for any assistance.
Consider the process: $dZ=r(t)Z\,dt$ , where $r(t)$ is stochastic and $Z=Z(r,t;T)$ is a zero coupon bond. Provide a bond pricing differential equation and invoke Feynman-Kac to show the solution requires the risk neutral measure $\mathbb{Q}$:
$$ Z(r,t;T)=\mathbb{E_Q}\left[\exp\left({-\int^T_tr(s)\,ds} \right)\right]. $$
Everything I read suggests write the PDE associated with $Z(r,t;T)$, integrate it and then take the expected value. I am stuck however on the first step as $dZ$ does not look like the usual Brownian motion with drift and diffusion? Thanks