 = \E^{\P_{0,F}} \left[ \phi\Big( X_{t_0\wedge \widetilde{\tau}}^{\alpha,\beta}, \dots, X_{t_n\wedge \widetilde{\tau}}^{\alpha,\beta} \Big) \E^{\P_{0,F}} \left[ \psi\Big( X_{t_0}^{\alpha,\beta}, \dots, X_{t_k}^{\alpha,\beta}, X_{t_{k+0}}^{\alpha,\beta}, \dots, X_{t_n}^{\alpha,\beta} \Big) | \mathcal{F}_{\widetilde{\tau}} \right]