This exercise demonstrates that the conclusion of Corollary 3.13 cannot be extended to sub martingales. Find a filtration {Ft} satisfying the usual conditions and a sub martingale X with respect to {F...

This exercise demonstrates that the conclusion of Corollary 3.13 cannot be extended to sub martingales. Find a filtration {Ft} satisfying the usual conditions and a sub martingale X with respect to {F_t} such that X does not have a version with paths that are right continuous with left limits.