As an application of the absolute continuity relationship between a BESQ and a CIR, prove that

\[\begin{equation*}{ }^{k} \mathbb{Q}_{x \rightarrow y}^{\delta, t}=\frac{\exp \left(-\frac{k^{2}}{2} \int_{0}^{t} ho_{s} d s\right)}{\mathbb{Q}_{x \rightarrow y}^{\delta, t}\left[\exp \left(-\frac{k^{2}}{2} \int_{0}^{t} ho_{s} d s\right)\right]} \mathbb{Q}_{x \rightarrow y}^{\delta, t} \tag{6.5.4}\end{equation*}\]

where \({ }^{k} \mathbb{Q}_{x \rightarrow y}^{\delta,(t)}\) denotes the bridge for \(\left(ho_{u}, 0 \leq u \leq t\right)\) obtained by conditioning \({ }^{k} \mathbb{Q}_{x}^{\delta}\) by \(\left(ho_{t}=y\right)\).