Moderate deviation principle for exponentially ergodic Markov chain

dc.creatorDelyon, B.
dc.creatorJuditsky, A.
dc.creatorLiptser, R.
dc.date2004-05-09
dc.date.accessioned2026-07-07T05:08:03Z
dc.date.available2026-07-07T05:08:03Z
dc.descriptionFor ${1/2}<α<1$, we propose the MDP analysis for family $$ S^α_n=\frac{1}{n^α}\sum_{i=1}^nH(X_{i-1}), n\ge 1, $$ 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 $\frac{1}{n^α}M_n$ with a martingale $M_n$ while the second to avoid the direct Laplace transform analysis.
dc.description16 pg
dc.identifierhttps://arxiv.org/abs/math/0405152
dc.identifierhttp://arxiv.org/abs/math/0405152
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71109
dc.subjectProbability
dc.subject60J27,60F10
dc.titleModerate deviation principle for exponentially ergodic Markov chain
dc.typetext

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