Causality between stopped filtrations and some applications

Abstract

In this paper we consider the concept of statistical causality in continuous time between filtrations associated with stopping times, which is based on Granger’s definition of causality. Especially, we consider a generalization of a causality relationship “His a cause of E within F” from fixed to stopping time. Then we apply the given concept of causality to strongly orthogonal stopped martingales. We show the equivalence between the given concept of causality and orthogonality of stopped local martingales, too.