标题： 离散状态空间上一般马尔可夫链的大偏差 显示英文标题

标题： Large deviations for general Markov chains on discrete state spaces

摘要： 我们研究在仅假设状态空间是离散的条件下马尔可夫链的大偏差。 特别是，我们不要求通常的不可约性和指数紧性假设。 使用次可加论证，我们提供了水平-2和水平-3大偏差原理的初等且自包含的证明。 由于马尔可夫链可能具有可约性，速率函数可能是非凸的，并且在特定集合之外可能与Donsker-Varadhan熵和其他经典速率函数不同。 显示英文摘要

摘要： We study the large deviations of Markov chains under the sole assumption that the state space is discrete. In particular, we do not require any of the usual irreducibility and exponential tightness assumptions. Using subadditive arguments, we provide an elementary and self-contained proof of the level-2 and level-3 large deviation principles. Due to the possible reducibility of the Markov chain, the rate functions may be nonconvex and may differ, outside a specific set, from the Donsker-Varadhan entropy and other classical rate functions.