Stable limits for Markov chains via the Principle of Conditioning.

We study limit theorems for partial sums of instantaneous functions of a homogeneous Markov chain on a general state space. The summands are heavy-tailed and the limits are stable distributions. We show that if the transition operator of the chain is operator uniformly integrable and the chain is ρ -mixing, then the limit is the same as if the summands were independent. We provide an example of a Markov chain that is operator uniformly integrable (and admits a spectral gap) while it is not hyperbounded. What makes our assumptions working is a new, efficient version of the Principle of Conditioning. [ABSTRACT FROM AUTHOR]