Moderate deviation principle for exponentially ergodic Markov chain
| dc.creator | Delyon, B. | |
| dc.creator | Juditsky, A. | |
| dc.creator | Liptser, R. | |
| dc.date | 2004-05-09 | |
| dc.date.accessioned | 2026-07-07T05:08:03Z | |
| dc.date.available | 2026-07-07T05:08:03Z | |
| dc.description | For ${1/2}<α<1$, 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.description | 16 pg | |
| dc.identifier | https://arxiv.org/abs/math/0405152 | |
| dc.identifier | http://arxiv.org/abs/math/0405152 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71109 | |
| dc.subject | Probability | |
| dc.subject | 60J27,60F10 | |
| dc.title | Moderate deviation principle for exponentially ergodic Markov chain | |
| dc.type | text |