Interconnection of Stochastic Systems

We address the interconnection of stochastic systems. A stochastic system is defined as a probability triple. The specification of the set of events is an essential part of a stochastic model. Models often require a coarse event sigma-algebra. A stochastic system is linear if the events are cylinders with fibers parallel to a linear subspace of a vector space. Two stochastic systems can be interconnected if they are complementary. We discuss aspects of the identification problem from this vantage point.