Abstract
For a Harris ergodic Markov chain (X n ) n ≥ 0, on a general state space, started from the small measure or from the stationary distribution, we provide optimal estimates for Orlicz norms of sums ∑ i = 0 τ f(X i ), where τ is the first regeneration time of the chain. The estimates are expressed in terms of other Orlicz norms of the function f (with respect to the stationary distribution) and the regeneration time τ (with respect to the small measure). We provide applications to tail estimates for additive functionals of the chain (X n ) generated by unbounded functions as well as to classical limit theorems (CLT, LIL, Berry-Esseen).
Mathematics Subject Classification (2010). Primary 60J05, 60E15; Secondary 60K05, 60F05
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Research partially supported by MNiSW Grant N N201 608740 and the Foundation for Polish Science.
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Adamczak, R., Bednorz, W. (2016). Orlicz Integrability of Additive Functionals of Harris Ergodic Markov Chains. In: Houdré, C., Mason, D., Reynaud-Bouret, P., Rosiński, J. (eds) High Dimensional Probability VII. Progress in Probability, vol 71. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-40519-3_13
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