论文标题
在离散时间不精确的Markov链中的上层和下预期时间平均值的限制行为
Limit Behaviour of Upper and Lower Expected Time Averages in Discrete-Time Imprecise Markov Chains
论文作者
论文摘要
我们研究了马尔可夫链中的上限和下限对预期时间平均的极限行为；马尔可夫链的一般类型，传统上以过渡概率为特征的局部动力学现在由“合理”过渡概率的集合表示。我们的主要结果是一组必要和充分的条件，在这些条件下，这些上限和下限（称为上和下限）将随着时间的流逝而趋向于无限限制，以限制不取决于该过程的初始状态的值。值得注意的是，我们的条件比为所谓的上限和稳定状态建立相似结果所需的条件要弱得多，而这些限制的上和较低期望也经常用于提供有关时间平均限制行为的近似信息。我们表明，这样的近似值是亚最佳选择，并且可以通过直接使用上层和较低的预期时间平均值来显着改善它。
We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now represented by sets of 'plausible' transition probabilities. Our main result is a set of necessary and sufficient conditions under which these upper and lower bounds, called upper and lower expected time averages, will converge as time progresses towards infinity to limit values that do not depend on the process' initial state. Remarkably, our conditions are considerably weaker than those needed to establish similar results for so-called limit -- or steady state -- upper and lower expectations, which are often used to provide approximate information about the limit behaviour of time averages as well. We show that such an approximation is sub-optimal and that it can be significantly improved by directly using upper and lower expected time averages.
