Granger causality and stopping times

We consider causality relationships between sigma-fields (filtrations) associated by stopping times, which can be applied to the stopped processes. These results are motivated by the causality relationship between filtrations "( t) is a cause of (a"< t) within (Ft)" and which is based on Granger's definition of causality. Then we give some basic properties of causality up to some stopping time. The given concept of causality associated to stopping times is equivalent with the preservation of the martingale property for the stopped processes when the filtration is getting larger.