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Asymptotics of a Class of Markov Processes Which Are Not in General Irreducible
Let $\mathbf{\alpha}_n$ be a sequence of i.i.d. nondecreasing random maps on a subset $S$ of $\mathbb{R}^k$ into itself and let $X_0$ be a random variable with values in $S$ independent of the sequence $\mathbf{\alpha}_n$. Then $X_n \equiv \mathbf{\alpha}_n \cdots \mathbf{\alpha}_1X_0$ is a Markov process. Conditions for the existence of unique …