Statistical causality and martingale representation property with application to stochastic differential equations (Q2922947)

The authors study the causality concept and the martingale representation property of the local martingale. As it was known before, the given causality concept is equivalent to a generalization of the notion of weak uniqueness for weak solutions of stochastic differential equations, while in the paper it is proved that the concept of causality is equivalent to the preservation of the martingale representation property when the filtration is getting smaller. The decomposition of the martingale with respect to the smaller filtration as the semimartingale with respect to the larger filtration is given, and necessary and sufficient conditions, in terms of causality, for the preservation of the representation property under the change of measure are formulated.