Open stochastic systems

The problem of giving an adequate definition of an open stochastic system is addressed and motivated using examples. A stochastic system is defined as a probability triple on the outcome space. The collection of events is an essential part of a stochastic model and it is argued that for phenomena with as outcome space a finite dimensional vector space, the framework of classical random vectors with the Borel σ-algebra as events is inadequate even for elementary applications. A stochastic system is linear if the events are cylinders with fibers parallel to a linear subspace of a vector space. We also address interconnection of stochastic systems.