Predictability and uniqueness of weak solutions of the stochastic differential equations

Causality is a topic which receives much attention nowadays and it represents a prediction property in the context of possible reduction of available information in order to predict a given filtration. In this paper we define the concept of dependence between stochastic processes and between filtrations, named causal predictability, which is based on the Granger’s definition of causality. This definition extends the ones already given in the continuous time. Then, we provide some properties of the given concept.

Finally, we apply the concept of causal predictability to the processes of the diffusion type, more precisely, to the uniqueness of weak solutions of the stochastic differential equations.