Orlicz integrability of additive functionals of Harris ergodic Markov chains

Details Orlicz integrability of additive functionals of Harris ergodic Markov chains Orlicz integrability of additive functionals of Harris ergodic Markov chains

2012-01-17

arxiv.org/abs/1201.3567v1

Mathematics

Probability

Scientific paper

For a Harris ergodic Markov chain $(X_n)_{n\ge 0}$, on a general state space, started from the so called small measure or from the stationary distribution we provide optimal estimates for Orlicz norms of sums $\sum_{i=0}^\tau f(X_i)$, where $\tau$ is the first regeneration time of the chain. The estimates are expressed in terms of other Orlicz norms of the function $f$ (wrt the stationary distribution) and the regeneration time $\tau$ (wrt 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).

Affiliated with

Also associated with

No associations

Rating

Orlicz integrability of additive functionals of Harris ergodic Markov chains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Orlicz integrability of additive functionals of Harris ergodic Markov chains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Orlicz integrability of additive functionals of Harris ergodic Markov chains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-97929