# Is this random walk well studied?

Suppose that we have an ergodic finite Markov chain $C$ with a fintie state space $S$, and we have random variables $X_s$ where $s\in S$. Consider the following random walk

$S_0=0$ and $S_{i+1}=S_i +X_{C_i}$.

(In words, the random walk $S$ is somehow time-inhomogeneous.)

Is the property of this random walk well studied? Can I get some reference. Thanks.

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29271: Any luck with an answer below? –  Did May 7 '12 at 12:16
$\color{red}{\text{0% accept rate}}$ –  Did Sep 15 '12 at 4:31