On a type of stochastic stability for a class of encoding schemes

It is shown for a class of symbol-by-symbol encoding schemes, including delta modulation and some adaptive quantization schemes, that the joint input-state-output sequence is asymptotically mean stationary if the input sequence is stationary. Asymptotic mean stationarity is also obtained for the sequence of outputs produced by a general kind of variable-length to variable-length scheme, as well as for some sequences of waiting times arising in queueing theory.