| Título: | Concentration inequalities for Markov processes via coupling |
| Autores: |
Redig, Frank; Mathematical Institute Leiden university Chazottes, Jean Rene; CPHT, Ecole Polytechnique, Paris |
| Fecha: | 2009-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
concentration inequalities, coupling, Markov processes 60J50, 60J10, 60F15 |
| Descripción: | We obtain moment and Gaussian bounds for general coordinate-wise Lipschitz functions evaluated along the sample path of a Markov chain. We treat Markov chains on general (possibly unbounded) state spaces via a coupling method. If the first moment of the coupling time exists, then we obtain a variance inequality. If a moment of order $1+a$ $(a > 0)$ of the coupling time exists, then depending on the behavior of the stationary distribution, we obtain higher moment bounds. This immediately implies polynomial concentration inequalities. In the case that a moment of order $1+ a$ is finite, uniformly in the starting point of the coupling, we obtain a Gaussian bound. We illustrate the general results with house of cards processes, in which both uniform and non-uniform behavior of moments of the coupling time can occur. |
| Idioma: | No aplica |
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