论文标题
连续时间不精确的链条链时间
Hitting Times for Continuous-Time Imprecise-Markov Chains
论文作者
论文摘要
我们研究了表征连续时间马尔可夫链的稳定概括的预期打击时间的问题。这种概括基于不精确概率的理论，而我们使用的模型基本上构成了一组随机过程。相对于这些集合中的变化，它们的推论是紧密的下限和上限。 我们考虑了这些模型的三种不同类型，这些类型对应于组成过程中不同级别的一般性和结构独立性假设。 我们的主要结果是双重的。首先，我们证明了所有三种类型的打击时间都是等效的。此外，我们表明这些推论是通过对众所周知的方程式线性系统的直接概括来描述的，该方程式是特征在于传统的时间均匀连续时间马尔可夫链的预期打击时间。
We study the problem of characterizing the expected hitting times for a robust generalization of continuous-time Markov chains. This generalization is based on the theory of imprecise probabilities, and the models with which we work essentially constitute sets of stochastic processes. Their inferences are tight lower- and upper bounds with respect to variation within these sets. We consider three distinct types of these models, corresponding to different levels of generality and structural independence assumptions on the constituent processes. Our main results are twofold; first, we demonstrate that the hitting times for all three types are equivalent. Moreover, we show that these inferences are described by a straightforward generalization of a well-known linear system of equations that characterizes expected hitting times for traditional time-homogeneous continuous-time Markov chains.
