Moderate deviation principle for exponentially ergodic Markov chain

Details Moderate deviation principle for exponentially ergodic Markov chain Moderate deviation principle for exponentially ergodic Markov chain

2004-05-09

arxiv.org/abs/math/0405152v1

Mathematics

Probability

16 pg

Scientific paper

For ${1/2}<\alpha<1$, we propose the MDP analysis for family $$ S^\alpha_n=\frac{1}{n^\alpha}\sum_{i=1}^nH(X_{i-1}), n\ge 1, $$ where $(X_n)_{n\ge 0}$ be a homogeneous ergodic Markov chain, $X_n\in \mathbb{R}^d$, when the spectrum of operator $P_x$ is continuous. The vector-valued function $H$ is not assumed to be bounded but the Lipschitz continuity of $H$ is required. The main helpful tools in our approach are Poisson equation and Stochastic Exponential; the first enables to replace the original family by $\frac{1}{n^\alpha}M_n$ with a martingale $M_n$ while the second to avoid the direct Laplace transform analysis.

Affiliated with

Also associated with

No associations

Rating

Moderate deviation principle for exponentially ergodic Markov chain 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 Moderate deviation principle for exponentially ergodic Markov chain, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Moderate deviation principle for exponentially ergodic Markov chain will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-41471