Causal predictability and weak solutions of the stochastic differential equations with driving semimartingales

Abstract

We consider causal relationships between σ-fields (filtrations) in continuous time and define the concept of dependence between filtrations, named causal predictability, which is based on the Granger's definition of causality. The concept of causality is analyzed using the tool of conditional independence. Then, we provide some properties of the given predictability concept. Finally, we apply the concept of causal predictability to the weak solutions of the stochastic differential equations (SDEs). © 2023 Elsevier B.V.