Abstract: One of the commonly used techniques in establishing ergodicity of a Markov chain has been developed in a series papers by Tweedie (1974, 1975) and his associates. The present paper intends to demonstrate a useful alternative technique originated by Benes (1967) in the context of continuous time Markov chains. This technique can be adapted to the case when a time series model observed at discrete time points is under consideration. One of the advantages of such a technique is that it enables us to drop off the crucial assumption of ψ-irreducibility as required by Tweedie's technique. Examples showing how to obtain stationarity conditions for bilinear models are given under finite and infinite variance assumptions on the noise sequence. Existence of moments is examined and finally, a central limit theorem and a law of the iterated logarithm concerning sample moments of some bilinear time series models are established.
Key words and phrases: Bilinear model, stationarity, central limit theorem, law of the iterated logarithm, moments.