 To overcome this obstacle, we elaborate our optional martingale representation results, which state that any local martingale in the large filtration stopped at the death time can be decomposed into several and precise orthogonal local martingales .
<clarity>  To overcome this obstacle, we elaborate our optional martingale representation results, which state that any local martingale in the large filtration stopped at the death time can be decomposed into several and precise orthogonal local martingales .
 To overcome this obstacle, we elaborate our optional martingale representation results, which state that any local martingale in the large filtration stopped at the death time can be decomposed into precise and unique orthogonal local martingales .