Serial dependence of a Markov process

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Abstract
Consider a Markov process defined in discrete time t = 1, 2, 3, hellip on a state space S. The state of the Process at time time t will be specifies by a random varable Vt, taking values in S. This paper presents some results concerning the behaviour of the saquence V1, V2, V3hellip, considered as a time series. In general, S will be assumed to be a Borel subset of an h-dimensional Euclideam space, where h is finite. The results apply, in particular, to a continuous state space, taking S to be an interval of the realine, or to discrete process having finitely or enumerably many states. Certain results, which are indicated in what follows, apply also to more general (infinite-dimensional) state spaces.

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