| Título: | Quantitative Convergence Rates of Markov Chains: A Simple Account |
| Autores: | Rosenthal, Jeffrey S.; University of Toronto |
| Fecha: | 2002-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Mathematics Markov chain, convergence rate, mixing time, drift condition, minorisation condition, total variation distance. Primary 60J05; secondary 62M05. |
| Descripción: | We state and prove a simple quantitative bound on the total variation distance after k iterations between two Markov chains with different initial distributions but identical transition probabilities. The result is a simplified and improved version of the result in Rosenthal (1995), which also takes into account the $epsilon$-improvement of Roberts and Tweedie (1999), and which follows as a special case of the more complicated time-inhomogeneous results of Douc et al. (2002). However, the proof we present is very short and simple; and we feel that it is worthwhile to boil the proof down to its essence. This paper is purely expository; no new results are presented. |
| Idioma: | Inglés |
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