  In many applications, the common assumption that a driving noise process
affecting a system is independent or Markovian may not be realistic, but the
noise process may be assumed to be stationary. To study such problems, this
paper investigates stochastic stability properties of a class of non-Markovian
processes, where the existence of a stationary measure, asymptotic mean
stationarity and ergodicity conditions are studied. Applications in feedback
quantization and stochastic control are presented.
