Statistical causality and local uniqueness for solutions of the martingale problem

Abstract

In this paper we consider the concept of statistical causality between filtrations associated with stopping times, which is based on Granger’s definition of causality. Especially, we consider a generalization of a causality relationship ”G is a cause of E within H” from fixed to stopping time. Then we apply the given causality concept to local uniqueness for the solution of the martingale problem. Also, we give some applications in finance.