Assuming an Affine term structure model, where bond prices arebe defined as: $$P(t,T)=\exp({A(t,T)-B(t,T)r_t)}$$ and describing the Q-dynamics of the short rate according to the model: $$dr_t=ar_tdt+\sigma dW_t$$hence having: $$ \partial_t{A(t,T)}=-\frac{\sigma^2}{2}B^2(t,T) \\\partial_tB(t,T)=-aB(t,T)-1$$ What is the Q-dynamics of the bond prices $dp(t,T)$?
Would it be correct to start from the P-dyanimics: $$ dp(t,T)=((B(t,T)+1)a+1)r_tp(t,T)dt-\sigma p(t,T)dW_t$$and perform the change of measure by defining the new Brownian motion as $$dW_t^{\mathcal{Q}}=dW_t-\frac{(B(t,T)+1)ar_t}{\sigma}dt$$