论文标题
马尔可夫连锁店的martingale minimax指数不平等
A martingale minimax exponential inequality for Markov chains
论文作者
论文摘要
我们证明了一种新的不平等，控制了马尔可夫链的经验度量的巨大偏差。这种不平等基于Donsker和Varadhan和Minimax定理使用的Martingale。它适用于凸组，并且需要在起点上提取最小值。在紧凑空间的情况下，这种不平等是对Donsker和Varadhan的大偏差估计的部分改善。在非紧凑空间的情况下，我们条件是该过程访问$ n $乘以空间的$ n $乘以$ n $ timples，并且我们仍然可以在指数尺度上获得控制。
We prove a new inequality controlling the large deviations of the empirical measure of a Markov chain. This inequality is based on the martingale used by Donsker and Varadhan and the minimax theorem. It holds for convex sets and it requires to take an infimum over the starting point. In the case of a compact space, this inequality is a partial improvement of the large deviations estimates of Donsker and Varadhan. In the case of a non compact space, we condition on the event that the process visits $n$ times a compact subset of the space and we still obtain a control on the exponential scale.
