论文标题
Markov更新过程的经验度量和经验流的大偏差，具有可数状态空间
Large deviations for the empirical measure and empirical flow of Markov renewal processes with a countable state space
论文作者
论文摘要
在这里，我们提出了Donsker-varadhan型紧凑性条件，并证明了Markov更新过程的经验度量和经验流的关节偏差原理（半摩尔多克过程）具有可数状态空间，从而概括了具有可计数的Markov链的相关结果，该结果具有可计数的Markov链，具有可计算的Markov链，具有可计算的Markov链。研究H.PoincaréProbab。统计学家。 51，867-900（2015）]和[Stoch。 Proc。应用。 125，2786-2819（2015）]，以及Markov更新过程的相关结果，并在[Adv。应用。概率。 48，648-671（2016）]。特别是，当流动空间赋予有限的弱*拓扑或强$ l^1 $拓扑时，我们的结果就会成立。即使是连续的马尔可夫连锁店，我们的紧凑条件也比以前的论文中提出的条件弱。此外，在某些更强的条件下，我们获得了经验流的边际速率函数的明确表达。
Here we propose the Donsker-Varadhan-type compactness conditions and prove the joint large deviation principle for the empirical measure and empirical flow of Markov renewal processes (semi-Markov processes) with a countable state space, generalizing the relevant results for continuous-time Markov chains with a countable state space obtained in [Ann. Inst. H. Poincaré Probab. Statist. 51, 867-900 (2015)] and [Stoch. Proc. Appl. 125, 2786-2819 (2015)], as well as the relevant results for Markov renewal processes with a finite state space obtained in [Adv. Appl. Probab. 48, 648-671 (2016)]. In particular, our results hold when the flow space is endowed with either the bounded weak* topology or the strong $L^1$ topology. Even for continuous-time Markov chains, our compactness conditions are weaker than the ones proposed in previous papers. Furthermore, under some stronger conditions, we obtain the explicit expression of the marginal rate function of the empirical flow.
