On ARMA (Autoregressive Moving Average) Representations for White Noise in a Markovian Environment.

Autoregressive moving average ARMA models are frequently used to describe disturbances associated with signals. Usually, such processes are discussed in the context of finite dimensional linear systems. In this note, the author shows, that ARMA models also occur in a rather different setting, namely as descriptions of white noise in a randomly varying environment. Such a result is useful in better understanding the proper role of ARMA processes in systems theory.