Lecture Notes in Computer Science: Statistical Causality and Local Solutions of the Stochastic Differential Equations Driven with Semimartingales

The paper considers a statistical concept of causality in continuous time between filtered probability spaces which is based on Granger’s definition of causality. Then, the given causality concept is connected with a local weak solutions of the stochastic differential equations driven with semimartingales. Also, we establish connection between the local solution and the local weak solution.