Randomized emulation of empirical systems

Random events may mimic a deterministic mechanism, e.g., by producing a nearly monotone relationship between dynamic variables that are independent insofar as the deterministic equations of a system are concerned. It is shown that the randomized emulation of linear systems does not produce effects that are independent of the deterministic linear equations. In the case of a linear system, y=M _x, randomized emulation simply converts monotone relations into parallel statistical trends, provided the sign of M does not change during randomization