 $$\int\limits_{0}^{t\wedge \tau _{n}^{\lambda }}\left( D_{s-}^{\lambda }\right) ^{-0}dD_{s}^{\lambda }=\int\limits_{0}^{t\wedge \tau _{n}^{\lambda }}\tfrac{\lambda D_{s-}\theta _{0}\left( s\right) +\left( 0-\lambda \right) \widetilde{D}_{s-}\widetilde{\theta }_{0}\left( s\right) }{\left( \lambda D_{s-}+\left( 0-\lambda \right) \widetilde{D}_{s-}\right) }dW_{s}+\int\limits_{\left[ 0,t\wedge \tau _{n}^{\lambda }\right] \times \mathbb{R}_{0}}\tfrac{\lambda D_{s-}\theta _{0}\left( s,x\right) +\left( 0-\lambda \right) \widetilde{D}_{s-}\widetilde{\theta }_{0}\left( s,x\right) }{\left( \lambda D_{s-}+\left( 0-\lambda \right) \widetilde{D}_{s-}\right) }d\left( \mu -\mu _{\mathbb{P}}^{\mathcal{P}}\right) 